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The value of tan^(-1)(1)+cos^(-1)(-1/2)+...

The value of `tan^(-1)(1)+cos^(-1)(-1/2)+sin^(-1)(-1/2)` is equal to

A

`(2pi)/(3)`

B

`-(pi)/(4)`

C

`(3pi)/(4)`

D

`(5pi)/(12)`

Text Solution

Verified by Experts

The correct Answer is:
C
`tan^(-1)(1)+cos^(-1)(-(1)/(2))+sin^(-1)(-(1)/(2))`
`=(pi)/(4)=pi-cos^(-1)((1)/(2))-sin^(-1)((1)/(2))`
`=(pi)/(4)+pi-(pi)/(3)-(pi)/(6)`
`=(3pi+12pi-4pi-2pi)/(12)=(9pi)/(12)`
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