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cos^(-1)("cos"(2cot^(-1)(sqrt(2)-1))) is...

`cos^(-1)("cos"(2cot^(-1)(sqrt(2)-1)))` is equal to

A

`sqrt(2)-1`

B

`(pi)/(4)`

C

`(3pi)/(4)`

D

0

Text Solution

Verified by Experts

The correct Answer is:
C
`cot^(-1)(sqrt(2)-1)=(pi)/(2)-tan^(-1)(sqrt(2)-1)=(pi)/2)-tan^(-1)("tan"(pi)/(8))`
`=(pi)/(2)-(pi)/(8)=(4pi-pi)/(8)=(3pi)/(8)`
`thereforecos^(-1)[cos{2*cot^(-1)(sqrt(2)-1)}]=cos^(-1)["cos{"{xx(3pi)/(8)}]`
`=cos^(-1)["cos"(3pi)/(4)]=(3pi)/(4)`
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