The solution of `sin^(-1)|sin x|=sqrt(sin^(-1)|sin x|)` is

Options

A. `n pi pm 1, n pi, n in Z`
B. `n pi+1, n pi, n in Z`
C. `n pi-1, n pi, n in Z`
D. `2n pi+1, n pi, n in Z`

Answer

A

Explanation

Solution of `y=sqrt(y)` is y = 1 and y = 0
`rArr sin^(-1)|sin x|=0` or 1
`sin^(-1)|sin x|` is periodic with period `pi`
In `(0, pi)`, if `sin^(-1)|sin x|=1, x = 1` or `x = pi -1`
`therefore` General solution is `x = n pi 1, n in Z`
If `sin^(-1)|sin x| =0 rArr x = n pi, n in Z`