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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) none of these

A

`sqrt2 -1`

B

`(pi)/(4)`

C

`(3pi)/(4)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
`cos^(-1) (cos (2 cot^(-1) (sqrt2 -1))) = cos^(-1) (cos (2(67.5^(@))))`
`= cos^(-1) (cos (135^(@)))`
`= 135^(@) = (3pi)/(4)`
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