Question
The general solution of the equation,
is :
Hint:
In this question, we have given an equation, that is.
![fraction numerator 1 minus sin x plus midline horizontal ellipsis. comma plus open parentheses 1 close parentheses to the power of n space sin to the power of n x plus midline horizontal ellipsis space. infinity over denominator 1 plus sin x plus midline horizontal ellipsis. comma plus space sin to the power of n x plus midline horizontal ellipsis space. infinity end fraction equals fraction numerator 1 minus cos 2 x over denominator 1 plus cos 2 x end fraction](data:image/png;base64,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)
We have to find the general solution of solution. We have given series of sine, put the sum to that and find the solution.
The correct answer is: ![left parenthesis negative 1 right parenthesis to the power of straight n pi divided by 6 plus straight n pi](data:image/png;base64,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)
Related Questions to study
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The noble gas used in atomic reactor ,is
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has
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,
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Number of solutions of the equation in the interval [0, 2
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Number of solutions of the equation in the interval [0, 2
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In this question, we have given equation, where we have to find where the θ belongs. For all value of sin θ cos θ = so θ always lies between ( 0 ,
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) .
If ![6 cos space 2 theta plus 2 cos squared space theta divided by 2 plus 2 sin squared space theta equals 0 comma negative pi less than theta less than pi comma text then end text theta equals](data:image/png;base64,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)
If ![6 cos space 2 theta plus 2 cos squared space theta divided by 2 plus 2 sin squared space theta equals 0 comma negative pi less than theta less than pi comma text then end text theta equals](data:image/png;base64,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)
The most general solution of the equations is
The most general solution of the equations is
The general solution of the equation, is
The general solution of the equation, is
The most general solution of cot =
and cosec
= – 2 is :
In this question, we have given cotθ = -√3 and cosecθ = -2. Where θ for both is -π/6 and then write the general solution.
The most general solution of cot =
and cosec
= – 2 is :
In this question, we have given cotθ = -√3 and cosecθ = -2. Where θ for both is -π/6 and then write the general solution.
Let S =
The sun of all distinct solution of the equation ![square root of 3 sec space x plus cosec space x plus 2 left parenthesis tan space x minus cot space x right parenthesis equals 0](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAS0AAAATCAYAAADF5FuHAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAABRBJREFUeNrtXHFkVlEUv2YymWlWksqSJJOMmjVr8pEkmUnRJEmZZNKfpaL0R+mPNZWYlSQVWWuSimQmScmaJFMm6Y/JWExqPl+9zrHfl9ftvnfve997b29998fP9t53v917zzn3nHvOu29CmKOc6BRACwsLi0Sxg9hvxWBhYTFT8JC4z4rBYhpxgHjGimHacQa6SDXmEr/ip4XFdGAV8bkVQ2rwDDpJLfYT7yruZ4gPiN+Jk8T3xE5ildWphQEaiT3ECWKWOETc6bNIaq3IUoPVxKcx/e0K4iXiC7AL9wKBa1nbPO5vJc5y3WPDemR1amGAAWKrmHrIw6iBc2qV2tXivhvjVnzGiEtWT+G8osYTYrPregvuGWMJcYxYFuA7E/+h4u0T0GRkVU18I907S2y3+kid7R4U0dcYtxPPK+53KoKZJw4TuwN0upQ47PNZP9JJr6MQPLDPSDevejjLRkRpbvOJuEszpr0ewj2Fz6JWvG58HDneISV6J0WVYpOVCpPSNe/cm6S/73ecphlpRRYli0aP8fECGUF/LKPFBmOLQj4iQVsKevQoyPwagu6ADMDlgo2K+xl8ZoTXxE0G7eYT98BINnu0eeWxQPOoh8Nj4ykhthE7FKkC7/xa0GY58YbB+AYxxjx4rBdjiFa68dVjoazE9UpcNxShrFRoUKSCE1IJQtfHDaSa+bG/VXx3O3Zw1a52A4ZjLFQ+ImFbCqoP0/nN8smqwp7dHFfoOt/XF/lmuaIhC2GUWKoxUDcP+bTlXUOlz+e9ii3gqMITHwxhAJtci3pDiAhhqnjd+HoQHeVo2VeEspJRhh2SvDPKFdBHCXYh8nczBu3iko9I2JacGPWfjXjOOZO+liG14ImtkxqdJp4z7KwSEYGNbr1HmxahLrTm8U3y8Kr6GF9XhBTIY4yNn1JVGSy8MJFCNz7VrkEVsYpBVrL99HmkBoU4LVVbJwJnO5NsyYlR/0k6rT9lg2NwWnwO66XU6CNxTcBOy+G4/D7vRv693FC5UaUehyDkMOdLnIjaOQGU/7/Lyl2/60MANV2cfn0cR5kiF1AuTkLyEQnbkhOT/uNID794pIdlqvSQT7j+ckXvtcQPmtRQ6xF9cAS5s5zPztZ8byzk7iF/JqhDBHgKEULxuvGZRsdikBVjBRzzbE3UbzTsowv1qrIYd1qFykckbEtOTPqPqxCvqqFvFB6FeK6j3MTvF4gnQnS6ClEuTK2Bd3y6JzDdIeo0HMnvYWHw7uWVCH4A1lTxuvGx4JsVqWBvEcqKA+Rtg8CoOvKQhVyEJkWO2mlFIR+RsC15yarQ+bVDN1Fiq1CfVrjq5UAvE3/AiMYQBf0wgKhWCqFkkFLuNhgcLzj5BWxOD0ZcdQ1+snNNIdRPmBz3uZB4xaefeWLq1L5b8FysvB7TQtSNrw5zrHE5+RHFTqIYZHXfwMYYqsOlQx5GPOxy5jxfflQ/it8LdVpRyUckbEtDhjvCoPOL63BpP9LTUuwcjwqfJ7tziD+Jd4TZe15NMLxJsF/8+zRDlefmIJwFijZ1MFBu81aoH/vXom6Wg0KafXLuXslg87glzI5yhIFufFuwuLKYY0uRyipIveO5VF/JoMbhKHb6g5Atz5uPBZyU6iFhnNZMtiUvWRUyvzhf46mEc55E9tcl1Kcb/vKeuqMLFhZJw74wnS6k6oXpOjitRVYvFikDv7hv/zXN9IPrWG1pG9Q2qxcLC4s04jfwRxKgYQ1DYwAAAUV0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bXNxcnQ+PG1uPjM8L21uPjwvbXNxcnQ+PG1pPnNlYzwvbWk+PG1vPiYjeEEwOzwvbW8+PG1pPng8L21pPjxtbz4rPC9tbz48bWk+Y29zZWM8L21pPjxtbz4mI3hBMDs8L21vPjxtaT54PC9taT48bW8+KzwvbW8+PG1uPjI8L21uPjxtbz4oPC9tbz48bWk+dGFuPC9taT48bW8+JiN4QTA7PC9tbz48bWk+eDwvbWk+PG1vPiYjeDIyMTI7PC9tbz48bWk+Y290PC9taT48bW8+JiN4QTA7PC9tbz48bWk+eDwvbWk+PG1vPik8L21vPjxtbz49PC9tbz48bW4+MDwvbW4+PC9tYXRoPj2LZ5UAAAAASUVORK5CYII=)
Let S =
The sun of all distinct solution of the equation ![square root of 3 sec space x plus cosec space x plus 2 left parenthesis tan space x minus cot space x right parenthesis equals 0](data:image/png;base64,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)
A wave motion has the function
The graph in figure shows how the displacement
at a fixed point varies with time
Which one of the labelled points shows a displacement equal to that at the position
at time ![t equals 0](data:image/png;base64,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)
![](data:image/png;base64,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)
A wave motion has the function
The graph in figure shows how the displacement
at a fixed point varies with time
Which one of the labelled points shows a displacement equal to that at the position
at time ![t equals 0](data:image/png;base64,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)
![](data:image/png;base64,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)
For
, the equation
has
For
, the equation
has
Which of the following pairs of compounds are functional isomers?
Which of the following pairs of compounds are functional isomers?
Let
be such that
and
Then
cannot satisfy
In this question we have to find the the which region ϕ cannot satisfy. In this question more than one option is correct. Here firstly solve the given equation. Remember that, , tan x + cot x = .
Let
be such that
and
Then
cannot satisfy
In this question we have to find the the which region ϕ cannot satisfy. In this question more than one option is correct. Here firstly solve the given equation. Remember that, , tan x + cot x = .