यदि `y=sin [2 tan^(-1)sqrt((1-x)/(1+x))]` तो `((dy)/(dx))` का मान ज्ञात कीजिये ।

Explanation

`y=sin[2 tan^(-1)sqrt((1-x)/(x+x))]`
`x=cos theta` रखने पर
`y = sin [ 2 tan^(-1) .sqrt((1-cos theta)/(1+cos theta))]`
`=sin [ 2tan^(-1)sqrt((2sin^(2)theta//2)/(2cos^(2)theta//2))]`
`=sin (2tan^(-1)tan.(theta)/(2) )=sin(2(theta)/(2))`
`=sin theta = sin (cos^(-1)x)`
`:. (dy)/(dx)=cos (cos^(-1)x)(-(1)/(sqrt(1-x^(2))))`
`=x(-(1)/(sqrt(1-x^(2))))=(-x)/(sqrt(1-x^(2)))`