Evaluate: (i) `intsin^(-1)(cosx)\ dx ,\ \ 0lt=xlt=pi`
(ii) `inttan^(-1){sqrt(((1-cos2x)/(1+cos2x)))}\ dx ,\ \ 0

Explanation

`\text { evaluate - i) } \int \sin ^{-1}(\cos x) d x`


`I=\int \sin ^{-1}[\sin (\frac{\pi}{2}-x)] d x`


`I=\int(\frac{\pi}{2}-x) d x`

`I=\frac{\pi}{2} x-\frac{x^{2}}{2}+c`


`\text { ii). } I=\int \tan ^{-1} \sqrt{\frac{1-\cos 2 x}{1+\cos 2 x}} d x`

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