Differentiate `cos^(-1)((1-x^(2n))/(1+x^(2n))),\ \ 0

Explanation

Solution:

Let `x^{n}=\tan \theta`

Now,

`y=\cos ^{-1}\{\frac{1-\tan ^{2} \theta}{1+\tan ^{2} \theta}} `

Using ` \frac{1-\tan ^{2} \theta}{1+\tan ^{2} \theta}=\cos 2 \theta`

`y=\cos ^{-1}\{\cos 2 \theta\}`

Considering the limits,

`0
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