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

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

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`

Text Solution

Verified by Experts

The correct Answer is:
A
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`
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