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IF tan ( pi cos theta) = cot ( pi sin...

IF ` tan ( pi cos theta) = cot ( pi sin theta )` then ` cos ( theta - (pi)/(4))` is equal to

A

`-cos theta int_(1)^(tan theta) f(x sin theta )dx`

B

`-tan theta int_(cos theta)^(sin theta) f(x)dx`

C

`sin theta int_(1)^(tan theta)f (x cos theta)dx`

D

`1/(tan theta) int_(sin theta)^(sin theta tan theta) f(x)dx`

Text Solution

Verified by Experts

The correct Answer is:
A
Putting `x tan theta =z sin theta` or `dx=cos theta dz`. We get
`I=cos theta int_(tan theta)^(1) f(z sin theta)dz`
`=-cos theta int_(1)^(tan theta)f(x sin theta) dx`
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CENGAGE-DEFINITE INTEGRATION -Exercise (Single)
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  11. IF tan ( pi cos theta) = cot ( pi sin theta ) then cos ( theta ...

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  13. L e tI1=int(-2)^2(x^6+3x^5+7x^4)/(x^4+2)dxa n d I2=int(-3)^1(2(x+1)^2...

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  14. Let f beintegrable over [0,a] for any real value of a. If I(1)=int(0...

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  16. IfI(m , n)=int0^1x^(m-1)(1-x)^(n-1)dx ,(m , n in I ,m ,ngeq0),t h e n...

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  17. The value of the definite integral int0^(pi/2)(sin5x)/(sinx)dxi s 0 (...

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  18. IfIn=int0^pie^x(sin"x")^("n")dx ,t h e n(I3)/(I1)i se q u a lto 3/5 ...

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  19. If f'(x)=f(x)+int(0)^(1)f(x)dx,given f(0)=1, then the value of f(log(e...

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  20. Let f(x) be positive, continuous, and differentiable on the interval ...

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