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The principal value of sin^-1 {tan ((-5p...

The principal value of `sin^-1 {tan ((-5pi)/4)}` is

A

`(pi)/(4)`

B

`-(pi)/(4)`

C

`(pi)/(2)`

D

`-(pi)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
D
`sin^(-1){tan((-5pi)/(1))}=sin^(-1){-tan(pi+(pi)/(4))}`
`=sin^(-1)(-"tan"(pi)/(4))`
`=sin^(-1)(-"sin"(pi)/(2))=-sin^(-1)("sin"(pi)/(2))`
`=-(pi)/(2)`
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