The value of `sin^(-1){cot(sin^(-1)sqrt((2-sqrt(3))/4)+cos^(-1)(sqrt(12))/4+sec^(-1)sqrt(2))}` is equal to `pi/4` (b) `pi/2` (c) 0 (d) `-pi/2`

Options

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

Explanation

`sin^(-1){cot(sin^(-1)sqrt(2-sqrt(3))/(4)+cos^(-1)sqrt(12)/(4)+sec^(-1)sqrt(2))}`
`=sin^(-1){cot(sin^(-1)sqrt(3)-1)/(2sqrt(2))+cos^(-1)sqrt(3)/(2)+sec^(-1)sqrt(2))}`
`sin^(-1){cost(pi)/(12)+(pi)/(6)+(pi)/(4)}=sin^(-1)(cot(pi)/(2))=sin^(-1)0=0`