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If x equals sec space theta plus tan space theta comma y equals cosec space theta minus cot space theta text  then  end text y equals

  1. fraction numerator 1 plus x over denominator 1 minus x end fraction
  2. fraction numerator 1 minus x over denominator 1 plus x end fraction
  3. fraction numerator x plus 1 over denominator x minus 1 end fraction
  4. fraction numerator x minus 1 over denominator x plus 1 end fraction

The correct answer is: fraction numerator x minus 1 over denominator x plus 1 end fraction

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For all values of theta,the values of 3 minus cos space theta plus cos space open parentheses theta plus pi over 3 close parentheses lie in the interval

For all values of theta,the values of 3 minus cos space theta plus cos space open parentheses theta plus pi over 3 close parentheses lie in the interval

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left parenthesis sin space x minus cos space x right parenthesis squared plus cos squared space open parentheses pi over 4 minus x close parentheses element of

left parenthesis sin space x minus cos space x right parenthesis squared plus cos squared space open parentheses pi over 4 minus x close parentheses element of

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5 cos space theta plus 3 cos space open parentheses theta minus pi over 3 close parentheses plus 8 element of

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cos space open parentheses x plus pi over 6 close parentheses cos space open parentheses x minus pi over 6 close parentheses element of

cos space open parentheses x plus pi over 6 close parentheses cos space open parentheses x minus pi over 6 close parentheses element of

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does not exist Extreme Values; cos space invisible function application x plus sin to the power of 4 space x element of

does not exist Extreme Values; cos space invisible function application x plus sin to the power of 4 space x element of

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left parenthesis sin space x plus cos space x right parenthesis squared plus cos squared space open parentheses pi over 4 plus x close parentheses element of

left parenthesis sin space x plus cos space x right parenthesis squared plus cos squared space open parentheses pi over 4 plus x close parentheses element of

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The minimum and maximum values of cos space x plus 3 square root of 2 sin space open parentheses x plus pi over 4 close parentheses plus 6 are

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Maths-General
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The minimum and maximum values of sin space open parentheses x plus pi over 4 close parentheses sin space open parentheses x minus pi over 4 close parentheses are

sin space open parentheses x plus pi over 4 close parentheses sin space open parentheses x minus pi over 4 close parentheses
equals sin squared x minus sin squared straight pi over 4
equals fraction numerator 1 minus cos 2 x over denominator 2 end fraction minus open parentheses fraction numerator 1 over denominator square root of 2 end fraction close parentheses squared
equals 1 half minus fraction numerator cos 2 x over denominator 2 end fraction minus 1 half
equals negative 1 half cos 2 x
F o r space m i n i m u m space v a l u e space o f space f left parenthesis x right parenthesis comma space cos 2 x equals 1
f left parenthesis x right parenthesis equals negative 1 half cross times 1 equals fraction numerator negative 1 over denominator 2 end fraction
F o r space m a x i m u m space v a l u e space o f space f left parenthesis x right parenthesis comma space cos 2 x equals negative 1
f left parenthesis x right parenthesis equals negative 1 half cross times negative 1 equals 1 half
S o comma space sin space open parentheses x plus pi over 4 close parentheses sin space open parentheses x minus pi over 4 close parentheses element of open square brackets fraction numerator negative 1 over denominator 2 end fraction comma 1 half close square brackets

The minimum and maximum values of sin space open parentheses x plus pi over 4 close parentheses sin space open parentheses x minus pi over 4 close parentheses are

Maths-General
sin space open parentheses x plus pi over 4 close parentheses sin space open parentheses x minus pi over 4 close parentheses
equals sin squared x minus sin squared straight pi over 4
equals fraction numerator 1 minus cos 2 x over denominator 2 end fraction minus open parentheses fraction numerator 1 over denominator square root of 2 end fraction close parentheses squared
equals 1 half minus fraction numerator cos 2 x over denominator 2 end fraction minus 1 half
equals negative 1 half cos 2 x
F o r space m i n i m u m space v a l u e space o f space f left parenthesis x right parenthesis comma space cos 2 x equals 1
f left parenthesis x right parenthesis equals negative 1 half cross times 1 equals fraction numerator negative 1 over denominator 2 end fraction
F o r space m a x i m u m space v a l u e space o f space f left parenthesis x right parenthesis comma space cos 2 x equals negative 1
f left parenthesis x right parenthesis equals negative 1 half cross times negative 1 equals 1 half
S o comma space sin space open parentheses x plus pi over 4 close parentheses sin space open parentheses x minus pi over 4 close parentheses element of open square brackets fraction numerator negative 1 over denominator 2 end fraction comma 1 half close square brackets
General
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sin squared space x plus cos to the power of 4 space x element of

sin squared space x plus cos to the power of 4 space x element of

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General
physics-

A piston fitted in cylindrical pipe is pulled as shown in the figure. A tuning fork is sounded at open end and loudest sound is heard at open length 13cm, 41 cm and 69 cm, the frequency of tuning fork if velocity of sound is 350 m s to the power of negative 1 end exponent is

In a closed organ pipe in which length of air-column can be increased or decreased, the first resonance occurs at lambda divided by 4 and second resonance occurs at 3 lambda divided by 4.
Thus, at first resonance
fraction numerator lambda over denominator 4 end fraction equals 13 blank horizontal ellipsis open parentheses i close parentheses
And a second resonance
fraction numerator 3 lambda over denominator 4 end fraction equals 41 blank horizontal ellipsis open parentheses i i close parentheses


Subtracting Eq.(i) from Eq.(ii), we have
fraction numerator 3 lambda over denominator 4 end fraction minus fraction numerator lambda over denominator 4 end fraction equals 41 minus 13
⟹ fraction numerator lambda over denominator 2 end fraction equals 28
therefore blank lambda equals 56 blank c m
Hence, frequency of tuning fork
v equals fraction numerator v over denominator lambda end fraction equals fraction numerator 350 over denominator 56 cross times 10 to the power of negative 2 end exponent end fraction equals 365 blank H z

A piston fitted in cylindrical pipe is pulled as shown in the figure. A tuning fork is sounded at open end and loudest sound is heard at open length 13cm, 41 cm and 69 cm, the frequency of tuning fork if velocity of sound is 350 m s to the power of negative 1 end exponent is

physics-General
In a closed organ pipe in which length of air-column can be increased or decreased, the first resonance occurs at lambda divided by 4 and second resonance occurs at 3 lambda divided by 4.
Thus, at first resonance
fraction numerator lambda over denominator 4 end fraction equals 13 blank horizontal ellipsis open parentheses i close parentheses
And a second resonance
fraction numerator 3 lambda over denominator 4 end fraction equals 41 blank horizontal ellipsis open parentheses i i close parentheses


Subtracting Eq.(i) from Eq.(ii), we have
fraction numerator 3 lambda over denominator 4 end fraction minus fraction numerator lambda over denominator 4 end fraction equals 41 minus 13
⟹ fraction numerator lambda over denominator 2 end fraction equals 28
therefore blank lambda equals 56 blank c m
Hence, frequency of tuning fork
v equals fraction numerator v over denominator lambda end fraction equals fraction numerator 350 over denominator 56 cross times 10 to the power of negative 2 end exponent end fraction equals 365 blank H z
General
physics-

In a sine wave, position of different particles at time t equals 0 is shown in figure. The equation for this wave travelling along positive x minus a x i s can be

As is clear from figure, att equals 0 comma x equals 0, displacementy equals 0. Therefore, option (a)or (d)may be correct.
In case of (d);y equals A sin invisible function application left parenthesis k x minus omega t right parenthesis
fraction numerator d y over denominator d t end fraction equals A cos invisible function application left parenthesis k x minus omega t right parenthesis open square brackets negative omega close square brackets
fraction numerator d y over denominator d x end fraction equals A cos invisible function application left parenthesis k x minus omega t right parenthesis open square brackets k close square brackets
fraction numerator fraction numerator d y over denominator d t end fraction over denominator d y divided by d x end fraction equals fraction numerator negative omega A cos invisible function application left parenthesis k x minus omega t right parenthesis over denominator k A cos invisible function application left parenthesis k x minus omega t right parenthesis end fraction equals negative fraction numerator omega over denominator k end fraction equals negative v
fraction numerator d y over denominator d t end fraction equals negative v open parentheses fraction numerator d y over denominator d x end fraction close parentheses
i e blank p a r t i c l e blank v e l o c i t y equals negative left parenthesis w a v e blank s p e e d right parenthesis cross times s l o p e.
And slope at x equals 0 and t equals 0is positive, in figure. Therefore, particle velocity is in negative y-direction.

In a sine wave, position of different particles at time t equals 0 is shown in figure. The equation for this wave travelling along positive x minus a x i s can be

physics-General
As is clear from figure, att equals 0 comma x equals 0, displacementy equals 0. Therefore, option (a)or (d)may be correct.
In case of (d);y equals A sin invisible function application left parenthesis k x minus omega t right parenthesis
fraction numerator d y over denominator d t end fraction equals A cos invisible function application left parenthesis k x minus omega t right parenthesis open square brackets negative omega close square brackets
fraction numerator d y over denominator d x end fraction equals A cos invisible function application left parenthesis k x minus omega t right parenthesis open square brackets k close square brackets
fraction numerator fraction numerator d y over denominator d t end fraction over denominator d y divided by d x end fraction equals fraction numerator negative omega A cos invisible function application left parenthesis k x minus omega t right parenthesis over denominator k A cos invisible function application left parenthesis k x minus omega t right parenthesis end fraction equals negative fraction numerator omega over denominator k end fraction equals negative v
fraction numerator d y over denominator d t end fraction equals negative v open parentheses fraction numerator d y over denominator d x end fraction close parentheses
i e blank p a r t i c l e blank v e l o c i t y equals negative left parenthesis w a v e blank s p e e d right parenthesis cross times s l o p e.
And slope at x equals 0 and t equals 0is positive, in figure. Therefore, particle velocity is in negative y-direction.
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The period of the function f left parenthesis x right parenthesis equals left square bracket 6 x plus 7 right square bracket plus cos space pi x minus 6 x where [.] de-notes the greatest integer function, is

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The period of the function open vertical bar sin cubed space x over 2 close vertical bar plus open vertical bar cos to the power of 5 space x over 5 close vertical bar is

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In any straight triangle A B C fraction numerator left parenthesis a plus b plus c right parenthesis left parenthesis b plus c minus a right parenthesis left parenthesis c plus a minus b right parenthesis left parenthesis a plus b minus c right parenthesis over denominator 4 b squared c squared end fraction =

In any straight triangle A B C fraction numerator left parenthesis a plus b plus c right parenthesis left parenthesis b plus c minus a right parenthesis left parenthesis c plus a minus b right parenthesis left parenthesis a plus b minus c right parenthesis over denominator 4 b squared c squared end fraction =

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