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

The value of `cos^(-1)(cos(2tan^(-1)((sqrt(3)+1)/(sqrt(4-2sqrt(3))))))`is

A

`(pi)/6`

B

`(5pi)/6`

C

`(5pi)/12`

D

`(pi)/12`

Text Solution

Verified by Experts

The correct Answer is:
B
`(sqrt(3)+1)/(sqrt(4-2sqrt(3)))=(sqrt(3)+1)/((sqrt(3)-1))=(sqrt(3)+1)/(sqrt(3)-1)=2+sqrt(3)="tan"(5pi)/12`
`:.cos^(-1)(cos(2.(5pi)/12))=cos^(-1)(cos(5pi)/6)=(5pi)/6`
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