The value of
`sin^(-1) (cot(sin^(-1) sqrt((2 -sqrt3)/(4)) + cos^(-1).(sqrt12)/(4) + sec^(-1) sqrt2))` is

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`