Question

`d/(dx)[sin^2cot^(- 1)sqrt((1-x)/(1+x))]` is
A. -1
B. `(1)/(2)`
C. `-(1)/(2)`
D. 1

Answer 1

`"Let "y=sin^(2)cot^(-1){sqrt((1-x)/(1+x))}`
`"Put "x=cos theta or theta = cos^(-1)x`
`therefore" "y=sin^(2)cot^(-1){sqrt((1-cos theta)/(1+cos theta))}= sin ^(2) cot^(-1) (tan""(theta)/(2))`
`=sin^(2)((pi)/(2)-(theta)/(2))`
`=cos^(2)((theta)/(2))`
`=(1+ cos theta)/(2)`
`=(1+x)/(2)`
`therefore" "(dy)/(dx)=(1)/(2)`