The value of `sin^(-1){cot(sin^(-1)(sqrt((2-sqrt3)/4)+cos^(-1)(sqrt(12)/4)+sec^(-1)sqrt2)}` is

Options

A. `0`
B. `(pi)/4`
C. `(pi)/6`
D. `(pi)/2`

Answer

D

Explanation

`sin^(-1)((sqrt(2-sqrt(3)))/2)=tan^(1)(sqrt((2-sqrt(3))/(2+sqrt(3))))=tan^(-1)(2-sqrt(3))`
`(pi)/12`
`cos^(-1)((sqrt(12))/4)=cos^(-1)((sqrt3)/2)=(pi)/6`
`impliessec^(-1)(sqrt(2))=(pi)/4`
`impliessin^(-1)((sqrt(2-sqrt(3)))/2)+cos^(-1)((sqrt(12))/4)+sec^(-1)(sqrt(2))`
`=(pi)/12+(pi)/6+(pi)/4+(pi)/2`
`implies "cot"(pi)/2=0` and `cos^(-1) (0)=(pi)/2`