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Evaluate: int(cos2x-cos2theta)/(cosx-cos...

Evaluate: `int(cos2x-cos2theta)/(cosx-costheta)dx`

A

`2(sinx+xcostheta) + C`

B

`2(sinx - xcos theta) + C`

C

`2(sinx+2xcostheta) + C`

D

`2(sinx-2x cos theta)+C`

Text Solution

Verified by Experts

The correct Answer is:
A
Let `I =int(cos2x -cos2theta)/(cosx - cos theta) dx`
`= int ((2cos^(2) x- 1 - 2 cos^(2) theta +1))/(cosx - cos theta)dx`
`= 2 int((cos x + cos theta) (cos x - cos theta))/((cosx - cos theta)) dx`
`= 2 int(cos x + cos theta) dx`
`= 2 (sinx + x cos theta) + C`
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