`d/(dx)[sin^2cot^(- 1)sqrt((1-x)/(1+x))]` is

Options

A. -1
B. `1/2`
C. `-(1)/(2)`
D. 1

Answer

B

Explanation

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