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The higher frequency TV broad casting bands range is

Solution for the question - the higher frequency tv broad casting bands range is 5.925 to 6.425 ghz and 3.7 to 4.2 ghz896 to 901 mhz and 840 to 935 mhz

The higher frequency tv broad casting bands range is-Turito

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A string of length <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAoAAAANCAYAAACQN/8FAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAFZJREFUeNpjYMAE34CYiYEAUAHiSwxEgAAgXk6MwnogLidG4SqoqQTBLSCWJqQI5NMvxJhmDsT7iVEYCcTziVE4CYgTiVG4Dog9iFH4Doj/48BsDMQCAHlSEYZSh/nGAAAASXRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaT5MPC9taT48L21hdGg+Bs5jnAAAAABJRU5ErkJggg==" class="Wirisformula" alt="L" width="10" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»L«/mi»«/math»'/> is fixed at one end and carries a mass <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAANCAYAAAB2HjRBAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAMNJREFUeNpjYEAFP4DYhQE/AMn/AWImZEEVIP4PxFPwaOQB4odAfAldIgCILwDxczyaZ0LVLEeXqAficiC+AcTmOJwLsrERqg4FrILa3grFyIALiG8BsQGSOhQAkpSG2noDTW4SkoE3oOrgABRy35D4IH9rQNnWQHwFiFmwqAMDkG370QKmHMm5xjjUgUEkEM9HC5yTQDwBzf/o6uB+SkPzxicgvgZ1Li51YLAOiL3QxBYjORefOoZ3QMzBQBgQq44wAAAH+yrmTEDtWAAAAEl0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+TTwvbWk+PC9tYXRoPttYuhkAAAAASUVORK5CYII=" class="Wirisformula" alt="M" width="15" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»M«/mi»«/math»'/> at the other end. The string makes <img src="data:image/png;base64,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" class="Wirisformula" alt="2 divided by pi" width="34" height="15" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mn»2«/mn»«mo»/«/mo»«mi»π«/mi»«/math»'/> revolutions per <img src="data:image/png;base64,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" class="Wirisformula" alt="s e c o n d" width="56" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»s«/mi»«mi»e«/mi»«mi»c«/mi»«mi»o«/mi»«mi»n«/mi»«mi»d«/mi»«/math»'/> around the vertical axis through the fixed end as shown in figure, then tension in the string is<img style="font-size: 1rem;" src="https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/903886/1/928100/Picture50.png" alt="" width="181" height="113" />

Solution for the question - a string of length l is fixed at one end and carries a mass m at the otherend. the string makes 2//pi revolutions per second around

A string of length l is fixed at one end and carries a mass m a-Turito

<img src="data:image/png;base64,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" class="Wirisformula" alt="cos invisible function application left parenthesis alpha minus beta right parenthesis equals 1 text  and  end text cos invisible function application left parenthesis alpha plus beta right parenthesis equals 1 over c" width="251" height="35" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»cos«/mi»«mo»§#8289;«/mo»«mo»(«/mo»«mi»§#945;«/mi»«mo»§#8722;«/mo»«mi»§#946;«/mi»«mo»)«/mo»«mo»=«/mo»«mn»1«/mn»«mtext»§#160;and§#160;«/mtext»«mi»cos«/mi»«mo»§#8289;«/mo»«mo»(«/mo»«mi»§#945;«/mi»«mo»+«/mo»«mi»§#946;«/mi»«mo»)«/mo»«mo»=«/mo»«mfrac»«mn»1«/mn»«mi»c«/mi»«/mfrac»«/math»'/> where <img src="data:image/png;base64,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" class="Wirisformula" alt="alpha comma beta element of left square bracket negative pi comma pi right square bracket" width="102" height="15" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#945;«/mi»«mo»,«/mo»«mi»§#946;«/mi»«mo»§#8712;«/mo»«mo»[«/mo»«mo»§#8722;«/mo»«mi»§#960;«/mi»«mo»,«/mo»«mi»§#960;«/mi»«mo»]«/mo»«/math»'/> Pairs <img src="data:image/png;base64,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" class="Wirisformula" alt="alpha comma beta" width="28" height="15" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#945;«/mi»«mo»,«/mo»«mi»§#946;«/mi»«/math»'/> which satisfy both the equations is/are

Solution for the question - cos(alpha-beta)=1 and cos(alpha+beta)=(1)/(c) where alpha,betain[-pi,pi] pairs alpha,beta which satisfy both theequations is/are 4

Cos(alpha-beta)=1 and cos(alpha+beta)=(1)/(c) where alpha,b-Turito

The number of integral values of k for which the equation <img src="data:image/png;base64,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" class="Wirisformula" alt="7 cos invisible function application x plus 5 sin invisible function application x equals 2 k plus 1" width="172" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»7«/mn»«mi»cos«/mi»«mo»§#8289;«/mo»«mi»x«/mi»«mo»+«/mo»«mn»5«/mn»«mi»sin«/mi»«mo»§#8289;«/mo»«mi»x«/mi»«mo»=«/mo»«mn»2«/mn»«mi»k«/mi»«mo»+«/mo»«mn»1«/mn»«/math»'/> has a solution is

Solution for the question - the number of integral values of k for which the equation 7cos x+5sinx=2k+1 has a solution is 121084

The number of integral values of k for which the equation 7cos -Turito

The number of distinct real roots of <img src="data:image/png;base64,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" class="Wirisformula" alt="open vertical bar table attributes columnalign center center center columnspacing 1em end attributes row cell sin invisible function application x end cell cell cos invisible function application x end cell cell cos invisible function application x end cell row cell cos invisible function application x end cell cell sin invisible function application x end cell cell cos invisible function application x end cell row cell cos invisible function application x end cell cell cos invisible function application x end cell cell sin invisible function application x end cell end table close vertical bar equals 0" width="190" height="70" style="vertical-align:-30px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨|¨ close=¨|¨ separators=¨|¨»«mtable columnspacing=¨1em¨ columnalign=¨center center center¨»«mtr»«mtd»«mi»sin«/mi»«mo»§#8289;«/mo»«mi»x«/mi»«/mtd»«mtd»«mi»cos«/mi»«mo»§#8289;«/mo»«mi»x«/mi»«/mtd»«mtd»«mi»cos«/mi»«mo»§#8289;«/mo»«mi»x«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»cos«/mi»«mo»§#8289;«/mo»«mi»x«/mi»«/mtd»«mtd»«mi»sin«/mi»«mo»§#8289;«/mo»«mi»x«/mi»«/mtd»«mtd»«mi»cos«/mi»«mo»§#8289;«/mo»«mi»x«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»cos«/mi»«mo»§#8289;«/mo»«mi»x«/mi»«/mtd»«mtd»«mi»cos«/mi»«mo»§#8289;«/mo»«mi»x«/mi»«/mtd»«mtd»«mi»sin«/mi»«mo»§#8289;«/mo»«mi»x«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»=«/mo»«mn»0«/mn»«/math»'/> in the interval <img src="data:image/png;base64,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" class="Wirisformula" alt="negative pi over 4 less or equal than x less or equal than pi over 4" width="98" height="31" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8722;«/mo»«mfrac»«mi»§#960;«/mi»«mn»4«/mn»«/mfrac»«mo»§#8804;«/mo»«mi»x«/mi»«mo»§#8804;«/mo»«mfrac»«mi»§#960;«/mi»«mn»4«/mn»«/mfrac»«/math»'/> is

Solution for the question - the number of distinct real roots of |[sin x,cos x,cos x],[cos x,sinx,cos x],[cos x,cos x,sin x]|=0 in the interval -(pi)/(4) 3

The number of distinct real roots of |[sin x,cos x,cos x],[co-Turito

If <img src="data:image/png;base64,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" class="Wirisformula" alt="0 less or equal than x less than 2 pi" width="76" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»0«/mn»«mo»§#8804;«/mo»«mi»x«/mi»«mo»§#60;«/mo»«mn»2«/mn»«mi»§#960;«/mi»«/math»'/>, then the number of real values of x, which satisfy the equation<img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAQAAAAANCAYAAABGm7AMAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAx5JREFUeNrtWkFkHGEUHhErKsJaFdVDiIqKiFyqYlWUWlERK+QQFVG9VuVaPfbSU0VViageqkKtqIooFauHHJaoqloRonKM0EMPsWKZvme/6Hj5Z+efZGaymTcfH5l/djbvm/+f73/vzTpOhihQJFaIf4nHxB/EB4r03yVuEI+IDeIucYlYULoepohuh8TSR3xDrIHLGMsQIb4R54i9OB4mbmFMA6rEGWLOMzZG/KJwLfAaqHeQAWwSp4U5bV72m+xeghgHiD8V63eQEWnTzzvsow6JcZb4yjC+ZNqcitjJOIXbJ84b0po6Uty6cJUTDGI3OMINMN0EvjkvDOPPcS7qBZCULhMaivXzNTvK9Bc9u6vfZ6LQbwsuS0s+JVvFEenaIbFM7CIOET94zt8m7hFHcDyC43Hxxds+N1DiO7Hfc/yQ+DqGHSBpXV6MowzQpr8fergPcF+R/hwyvgGLGMPqdy1owh9RlnljPZBO8STASaYMzvlJjLFD5i0mZpL4En/fO0NN4oZwwCR1naAHDZeiIv1yQS4qm3/e1R9bxnhe/bZotjl3LGu1voBaLmdwEVnjlUM0v74SJ5xWx7wQcnHZOuBF6MpjAZUU6y/DACeU6B81ZHtuhPMfhwE0wgTr2rgIwF3QFdRTQ22+cxHXj8bYBEpa1yAe/hsWsaVRv/x8TYn+mmHO3Qjn/6wGeOBTAvTIEuAwIqf04ilqHb9mSQVp0FyMCyBJXTexQK5YNqbSpj9wl0mx/rAP53n1h2kCThrGS7IJuGJRK00b0qK1Ntd0+Tgp75Kf8aD0osFSiGkBJKWLGzofid0WMaVRv19avKtYvxvj/NtiBvdA4p00Hg5qHxewwOvEt57zt5xWd3TYM7l7bZpcDH6lURVjV53WL8YKounyPqYFkJSudWQAQUirfn7NNgsD5P/Dr5l+ExeU6LeNMSr9YVBFudGN7OYZ5usUxlDLNNGYkM7Ige7A/X7BKf1qlSaEXhOp1RomQWLVJ1WJAnHrCkoBNei/AxNsgFXndHc9zfptDOCi9Odhejwv/DZj2fn/i9UMGTJoxj+0k7xQdlIowgAAASt0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+Y29zPC9taT48bW8+JiN4MjA2MTs8L21vPjxtaT54PC9taT48bW8+KzwvbW8+PG1pPmNvczwvbWk+PG1vPiYjeDIwNjE7PC9tbz48bW4+MjwvbW4+PG1pPng8L21pPjxtbz4rPC9tbz48bWk+Y29zPC9taT48bW8+JiN4MjA2MTs8L21vPjxtbj4zPC9tbj48bWk+eDwvbWk+PG1vPis8L21vPjxtaT5jb3M8L21pPjxtbz4mI3gyMDYxOzwvbW8+PG1uPjQ8L21uPjxtaT54PC9taT48bW8+PTwvbW8+PG1uPjA8L21uPjwvbWF0aD5TLle5AAAAAElFTkSuQmCC" class="Wirisformula" alt="cos invisible function application x plus cos invisible function application 2 x plus cos invisible function application 3 x plus cos invisible function application 4 x equals 0" width="256" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»cos«/mi»«mo»§#8289;«/mo»«mi»x«/mi»«mo»+«/mo»«mi»cos«/mi»«mo»§#8289;«/mo»«mn»2«/mn»«mi»x«/mi»«mo»+«/mo»«mi»cos«/mi»«mo»§#8289;«/mo»«mn»3«/mn»«mi»x«/mi»«mo»+«/mo»«mi»cos«/mi»«mo»§#8289;«/mo»«mn»4«/mn»«mi»x«/mi»«mo»=«/mo»«mn»0«/mn»«/math»'/> is :

If 0 -Turito

The number of solutions of the equation <img src="data:image/png;base64,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" class="Wirisformula" alt="cos squared invisible function application open parentheses x plus pi over 6 close parentheses plus cos squared invisible function application x minus 2 cos invisible function application open parentheses x plus pi over 6 close parentheses cos invisible function application open parentheses pi over 6 close parentheses equals sin squared invisible function application pi over 6" width="405" height="38" style="vertical-align:-14px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi»cos«/mi»«mn»2«/mn»«/msup»«mo»§#8289;«/mo»«mfenced separators=¨|¨»«mrow»«mi»x«/mi»«mo»+«/mo»«mfrac»«mi»§#960;«/mi»«mn»6«/mn»«/mfrac»«/mrow»«/mfenced»«mo»+«/mo»«msup»«mi»cos«/mi»«mn»2«/mn»«/msup»«mo»§#8289;«/mo»«mi»x«/mi»«mo»§#8722;«/mo»«mn»2«/mn»«mi»cos«/mi»«mo»§#8289;«/mo»«mfenced separators=¨|¨»«mrow»«mi»x«/mi»«mo»+«/mo»«mfrac»«mi»§#960;«/mi»«mn»6«/mn»«/mfrac»«/mrow»«/mfenced»«mi»cos«/mi»«mo»§#8289;«/mo»«mfenced separators=¨|¨»«mfrac»«mi»§#960;«/mi»«mn»6«/mn»«/mfrac»«/mfenced»«mo»=«/mo»«msup»«mi»sin«/mi»«mn»2«/mn»«/msup»«mo»§#8289;«/mo»«mfrac»«mi»§#960;«/mi»«mn»6«/mn»«/mfrac»«/math»'/> in the interval <img src="data:image/png;base64,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" class="Wirisformula" alt="left parenthesis negative pi divided by 2 comma pi divided by 2 right parenthesis" width="100" height="17" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mo»§#8722;«/mo»«mi»§#960;«/mi»«mo»/«/mo»«mn»2«/mn»«mo»,«/mo»«mi»§#960;«/mi»«mo»/«/mo»«mn»2«/mn»«mo»)«/mo»«/math»'/> is

Solution for the question - the number of solutions of the equationcos^(2)(x+(pi)/(6))+cos^(2)x-2cos(x+(pi)/(6))cos((pi)/(6))=sin^(2)(pi)/(6)in the interval (-p

The number of solutions of the equation cos^(2)(x+(pi)/(6))+cos-Turito

The possible values of <img src="data:image/png;base64,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" class="Wirisformula" alt="theta element of left parenthesis 0 comma pi right parenthesis" width="65" height="17" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#952;«/mi»«mo»§#8712;«/mo»«mo»(«/mo»«mn»0«/mn»«mo»,«/mo»«mi»§#960;«/mi»«mo»)«/mo»«/math»'/> such that<img src="data:image/png;base64,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" class="Wirisformula" alt="sin invisible function application theta plus sin invisible function application 4 theta plus sin invisible function application 7 theta equals 0" width="183" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»sin«/mi»«mo»§#8289;«/mo»«mi»§#952;«/mi»«mo»+«/mo»«mi»sin«/mi»«mo»§#8289;«/mo»«mn»4«/mn»«mi»§#952;«/mi»«mo»+«/mo»«mi»sin«/mi»«mo»§#8289;«/mo»«mn»7«/mn»«mi»§#952;«/mi»«mo»=«/mo»«mn»0«/mn»«/math»'/>  are :

Solution for the question - the possible values of theta in(0,pi) such that sin theta+sin 4theta+sin7theta=0 are : (pi)/(4),(5pi)/(2),(pi)/(2),(2pi)/(3),(3pi)/(4),(8pi)/(9)

The possible values of theta in(0,pi) such that sin theta+sin-Turito

The number of values of x in the interval [0, 3<img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAAKCAYAAACALL/6AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAAFRJREFUeNpjYIAAQSC+AMR/gPg/HgwHxkDcCsQs6BJA8IOBAKC/hj+ENPwhYAAKYMLihG9AzIZLgzwQf0ETOw7EtUCshU1DFhDvQBPzgtrSxUAOAAB9ShrRVe23BQAAAGR0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWkgbWF0aHZhcmlhbnQ9Im5vcm1hbCI+JiN4M0MwOzwvbWk+PC9tYXRoPgrR1l0AAAAASUVORK5CYII=" class="Wirisformula" alt="straight pi" width="12" height="10" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨normal¨»§#960;«/mi»«/math»'/>] satisfying the equation ,<img src="data:image/png;base64,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" class="Wirisformula" alt="2 sin squared invisible function application x plus 5 sin invisible function application x minus 3 equals 0" width="167" height="17" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»2«/mn»«msup»«mi»sin«/mi»«mn»2«/mn»«/msup»«mo»§#8289;«/mo»«mi»x«/mi»«mo»+«/mo»«mn»5«/mn»«mi»sin«/mi»«mo»§#8289;«/mo»«mi»x«/mi»«mo»§#8722;«/mo»«mn»3«/mn»«mo»=«/mo»«mn»0«/mn»«/math»'/> is

Solution for the question - the number of values of x in the interval [0, 3 pi ] satisfying theequation , 2sin^(2)x+5sin x-3=0 is 4216

The number of values of x in the interval [0, 3 pi ] satisfying-Turito

The number of solutions of tan x + sec x = 2 cos x in [0, 2<img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAAKCAYAAACALL/6AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAAFRJREFUeNpjYIAAQSC+AMR/gPg/HgwHxkDcCsQs6BJA8IOBAKC/hj+ENPwhYAAKYMLihG9AzIZLgzwQf0ETOw7EtUCshU1DFhDvQBPzgtrSxUAOAAB9ShrRVe23BQAAAGR0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWkgbWF0aHZhcmlhbnQ9Im5vcm1hbCI+JiN4M0MwOzwvbWk+PC9tYXRoPgrR1l0AAAAASUVORK5CYII=" class="Wirisformula" alt="straight pi" width="12" height="10" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨normal¨»§#960;«/mi»«/math»'/>], is

Solution for the question - the number of solutions of tan x + sec x = 2 cos x in [0, 2 pi ], is 103

The number of solutions of tan x + sec x = 2 cos x in [0, 2 pi -Turito

Over <img src="data:image/png;base64,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" class="Wirisformula" alt="left square bracket negative pi comma pi right square bracket" width="58" height="15" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»[«/mo»«mo»§#8722;«/mo»«mi»§#960;«/mi»«mo»,«/mo»«mi»§#960;«/mi»«mo»]«/mo»«/math»'/> the solution of <img src="data:image/png;base64,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" class="Wirisformula" alt="2 sin squared invisible function application open parentheses x plus pi over 4 close parentheses plus square root of 3 cos invisible function application 2 x greater or equal than 0" width="220" height="38" style="vertical-align:-14px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»2«/mn»«msup»«mi»sin«/mi»«mn»2«/mn»«/msup»«mo»§#8289;«/mo»«mfenced separators=¨|¨»«mrow»«mi»x«/mi»«mo»+«/mo»«mfrac»«mi»§#960;«/mi»«mn»4«/mn»«/mfrac»«/mrow»«/mfenced»«mo»+«/mo»«msqrt»«mn»3«/mn»«/msqrt»«mi»cos«/mi»«mo»§#8289;«/mo»«mn»2«/mn»«mi»x«/mi»«mo»§#8805;«/mo»«mn»0«/mn»«/math»'/> is

Solution for the question - over [-pi,pi] the solution of 2sin^(2)(x+(pi)/(4))+sqrt3cos 2x >= 0 is [-pi,(-7pi)/(12)]uu[-(pi)/(4),(5pi)/(12)]uu[(3pi)/(4),pi] [0,pi]

Over [-pi,pi] the solution of 2sin^(2)(x+(pi)/(4))+sqrt3cos 2-Turito

Solution to inequality cos 2x + 5 cos x + 3 ≥ 0 over <img src="data:image/png;base64,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" class="Wirisformula" alt="left square bracket negative pi comma pi right square bracket" width="58" height="15" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»[«/mo»«mo»§#8722;«/mo»«mi»§#960;«/mi»«mo»,«/mo»«mi»§#960;«/mi»«mo»]«/mo»«/math»'/> is

Solution for the question - solution to inequality cos 2x + 5 cos x + 3 0 over [-pi,pi] is [(-2pi)/(3),(2pi)/(3)] [0,-pi] [(-5pi)/(6),(5pi)/(6)] [-pi,pi]

Solution to inequality cos 2x + 5 cos x + 3 0 over [-pi,pi-Turito

Let <img src="data:image/png;base64,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" class="Wirisformula" alt="f left parenthesis x right parenthesis equals fraction numerator c o s e c to the power of 4 end exponent invisible function application x minus 2 c o s e c to the power of 2 end exponent invisible function application x plus 1 over denominator c o s e c invisible function application x left parenthesis c o s e c invisible function application x minus s i n invisible function application x right parenthesis plus fraction numerator s i n invisible function application x minus c o s invisible function application x over denominator sin invisible function application x end fraction plus c o t invisible function application x end fraction" width="370" height="53" style="vertical-align:-26px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mfrac»«mrow»«msup»«mrow»«mi»c«/mi»«mi»o«/mi»«mi»s«/mi»«mi»e«/mi»«mi»c«/mi»«/mrow»«mrow»«mn»4«/mn»«/mrow»«/msup»«mo»⁡«/mo»«mi»x«/mi»«mo»-«/mo»«mn»2«/mn»«msup»«mrow»«mi»c«/mi»«mi»o«/mi»«mi»s«/mi»«mi»e«/mi»«mi»c«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«mo»⁡«/mo»«mi»x«/mi»«mo»+«/mo»«mn»1«/mn»«/mrow»«mrow»«mi»c«/mi»«mi»o«/mi»«mi»s«/mi»«mi»e«/mi»«mi»c«/mi»«mo»⁡«/mo»«mi»x«/mi»«mo»(«/mo»«mi»c«/mi»«mi»o«/mi»«mi»s«/mi»«mi»e«/mi»«mi»c«/mi»«mo»⁡«/mo»«mi»x«/mi»«mo»-«/mo»«mi»s«/mi»«mi»i«/mi»«mi»n«/mi»«mo»⁡«/mo»«mi»x«/mi»«mo»)«/mo»«mo»+«/mo»«mfrac»«mrow»«mi»s«/mi»«mi»i«/mi»«mi»n«/mi»«mo»⁡«/mo»«mi»x«/mi»«mo»-«/mo»«mi»c«/mi»«mi»o«/mi»«mi»s«/mi»«mo»⁡«/mo»«mi»x«/mi»«/mrow»«mrow»«mrow»«mrow»«mi»sin«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mi»x«/mi»«/mrow»«/mrow»«/mrow»«/mfrac»«mo»+«/mo»«mi»c«/mi»«mi»o«/mi»«mi»t«/mi»«mo»⁡«/mo»«mi»x«/mi»«/mrow»«/mfrac»«/math»'/> The sum of all the solutions of f (x) = 0 in [0, 100p] is

Solution for the question - let f(x)=(cosec^(4)x-2cosec^(2)x+1)/(cosec x(cosec x-sin x)+(sin x-cosx)/(sin x)+cot x) the sum of all the solutions of f (x) = 0 in

Let f(x)=(cosec^(4)x-2cosec^(2)x+1)/(cosec x(cosec x-sin x)+(si-Turito

We know that tan x · tan 2x · tan 3x = tan 3x – tan 2x – tan x hence tan x + tan 2x + tan 3x = tan 3x – tan 2x – tan x Þ tan x + tan 2x = 0 \ tan 2x = tan (– x) 2x = np – x <img src="data:image/png;base64,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" class="Wirisformula" alt="x equals fraction numerator n pi over denominator 3 end fraction comma n element of I" width="97" height="32" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»x«/mi»«mo»=«/mo»«mfrac»«mrow»«mi»n«/mi»«mi»π«/mi»«/mrow»«mrow»«mn»3«/mn»«/mrow»«/mfrac»«mo»,«/mo»«mi»n«/mi»«mo»∈«/mo»«mi»I«/mi»«/math»'/>

The general solution of the trigonometric equation tan x + tan 2x + tan 3x = tan x · tan 2x tan 3x is where n <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAAMCAYAAABr5z2BAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAALV/ZLFgAAAGNJREFUeNpjYMANNIB4AhCfA+JvQPwLiP8zEAmCgPgKEGcAsTEQszGQAGShtnIxkAkmAXEAAwXgKRAzUWIALLBwYdq7YAKlYQCKhTNAzEOJIeFI6cAAiFnIMQQ9Jf4hJSUSDQC2pRnou82QIwAAAFB0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW8+JiN4MjIwODs8L21vPjwvbWF0aD4h58XOAAAAAElFTkSuQmCC" class="Wirisformula" alt="element of" width="16" height="12" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8712;«/mo»«/math»'/> I

Solution for the question - the general solution of the trigonometric equation tan x + tan 2x + tan 3x= tan x  tan 2x tan 3x is where n e i x=(n pi)/(3)

The general solution of the trigonometric equation tan x + tan -Turito

For the given relation cos q = (2 sin q cos q) sin q, sin q¹ 0 <img src="data:image/png;base64,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" class="Wirisformula" alt="table row cell text end text text o end text text r end text text end text s i n invisible function application theta equals plus-or-minus fraction numerator 1 over denominator square root of 2 end fraction text end text text o end text text r end text text end text c o s invisible function application theta equals 0 end cell row cell text end text text o end text text r end text text end text theta equals fraction numerator pi over denominator 4 end fraction comma fraction numerator 3 pi over denominator 4 end fraction comma fraction numerator pi over denominator 2 end fraction end cell end table" width="225" height="86" style="vertical-align:-38px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mtable»«mtr»«mtd»«mrow»«maligngroup/»«malignmark/»«mtext» «/mtext»«mtext»o«/mtext»«mtext»r«/mtext»«mtext» «/mtext»«mi»s«/mi»«mi»i«/mi»«mi»n«/mi»«mo»⁡«/mo»«mi»θ«/mi»«mo»=«/mo»«mo»±«/mo»«mfrac»«mrow»«mn»1«/mn»«/mrow»«mrow»«msqrt»«mn»2«/mn»«/msqrt»«/mrow»«/mfrac»«mtext» «/mtext»«mtext»o«/mtext»«mtext»r«/mtext»«mtext» «/mtext»«mi»c«/mi»«mi»o«/mi»«mi»s«/mi»«mo»⁡«/mo»«mi»θ«/mi»«mo»=«/mo»«mn»0«/mn»«/mrow»«/mtd»«/mtr»«mtr»«mtd»«mrow»«maligngroup/»«malignmark/»«mtext» «/mtext»«mtext»o«/mtext»«mtext»r«/mtext»«mtext» «/mtext»«mi»θ«/mi»«mo»=«/mo»«mfrac»«mrow»«mi»π«/mi»«/mrow»«mrow»«mn»4«/mn»«/mrow»«/mfrac»«mo»,«/mo»«mfrac»«mrow»«mn»3«/mn»«mi»π«/mi»«/mrow»«mrow»«mn»4«/mn»«/mrow»«/mfrac»«mo»,«/mo»«mfrac»«mrow»«mi»π«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/mfrac»«/mrow»«/mtd»«/mtr»«/mtable»«/math»'/> Then the sum of roots is 3p/2

The sum of all the solution of cotθ= sin 2θ(θ ≠ n<img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAAKCAYAAACALL/6AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAAFRJREFUeNpjYIAAQSC+AMR/gPg/HgwHxkDcCsQs6BJA8IOBAKC/hj+ENPwhYAAKYMLihG9AzIZLgzwQf0ETOw7EtUCshU1DFhDvQBPzgtrSxUAOAAB9ShrRVe23BQAAAGR0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWkgbWF0aHZhcmlhbnQ9Im5vcm1hbCI+JiN4M0MwOzwvbWk+PC9tYXRoPgrR1l0AAAAASUVORK5CYII=" class="Wirisformula" alt="straight pi" width="12" height="10" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨normal¨»§#960;«/mi»«/math»'/>, n integer), 0 ,<img src="data:image/png;base64,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" class="Wirisformula" alt="less or equal than theta less or equal than pi" width="56" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8804;«/mo»«mi»§#952;«/mi»«mo»§#8804;«/mo»«mi»§#960;«/mi»«/math»'/> is

Solution for the question - the sum of all the solution of cotq = sin 2q (q  np, n integer), 0qp, is 2 pi  infinitepi 3 pi /2

The sum of all the solution of cotq = sin 2q (q  np, n intege-Turito

Solution for the question - General 014'/>