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The value of sin^(-1)("cos"(cos^(-1)(cos...

The value of `sin^(-1)("cos"(cos^(-1)(cosx)+sin^(-1)(sinx))),` where `x in (pi/2,pi)` , is equal to `pi/2` (b) `-pi` (c) `pi` (d) `-pi/2`

A

`(pi)/(2)`

B

`-pi`

C

`pi`

D

`-(pi)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
D
`sin^(-1) (cos (cos^(-1) (cos x) + sin^(-1) (sin x)))`
`= sin^(-1) (cos (x + pi - x)) " " ["as " x in (pi//2)]`
`= sin^(-1) (cos pi) = sin^(-1) (-1) = -(pi)/(2)`
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