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What is the value of cos^(-1)(cos((2pi)/...

What is the value of `cos^(-1)(cos((2pi)/3))+sin^(-1)(sin((2pi)/3))` ?

A

`(4pi)/3`

B

`pi/2`

C

`(3pi)/4`

D

`pi`

Text Solution

Verified by Experts

The correct Answer is:
D
`cos^(-1)(cos(2pi)/3)=sin^(-1)(sin(2pi)/3)`
`=cos^(-1){cos(pi-pi/3)}+sin^(-1){sin(pi-pi/3)}`
`=cos^(-1)(-cospi/3)+sin^(-1){sinpi/3}=cos^(-1)(-1/2)+pi/3`
`=((2pi)/3+pi/3)=pi`.
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