Write each of the following in the simplest form:

(i)`sin^(-1){(sqrt(1+x)+sqrt(1-x))/2},\ \ 0 < x <1`

(ii)`sin{2tan^(-1)(sqrt((1-x)/(1+x)))}`

Explanation

(i)


Let `x=\cos \theta`



Now,



`\sin ^{-1}\{\frac{\sqrt{1+x}+\sqrt{1-x}}{2}\}=\sin ^{-1}\{\frac{\sqrt{1+\cos \theta}+\sqrt{1-\cos \theta}}{2}\}`



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