If ` y = sin^(-1) x + sin^(-1) sqrt(1 - x^(2)), - 1 le x le 1," then " (dy)/(dx)` is

Options

A. 0
B. `(pi)/(2)`
C. 1
D. 4

Answer

A

Explanation

Given , ` y = sin^(-1) x sin^(-1) sqrt(1 - x^(2))`
On putting ` x = sin theta rArr theta = sin^(-1) x ` , we get
`rArr y = theta + sin^(-1) sqrt(1 - sin^(2) theta )`
`rArr y = theta + sin^(-1) (cos theta)`
`rArr y = theta + sin^(-1) (sin"(pi)/(2) - theta)`
` rArr y = theta + (pi)/(2)-theta = (pi)/(2)`
On differentiating both sides w.r.t.x, we get
` (dy)/(dx) = 0`