The value of `sin^(-1)("cot"(sin^(-1)sqrt((2-sqrt(3))/4)+cos^(-1)((sqrt(12))/4)+sec^(-1)sqrt(2)))i s` (a)`0` (b) `pi/2` (c) `pi/3` (d) none of these

Options

A. 0
B. `(pi)/(2)`
C. `(pi)/(3)`
D. none of these

Answer

A

Explanation

We have
`sin^(-1) (cot (sin^(-1) sqrt((2-sqrt3)/(4)) + cos^(-1). (sqrt12)/(4) + sec^(-1) sqrt2))`
`= sin^(-1) (cot (sin^(-1) ((sqrt3 -1)/(2sqrt2)) + cos^(-1).(sqrt3)/(2) + cos^(-1).(1)/(sqrt2)))`
`= sin^(-1) [cot (15^(@) + 30^(@) + 45^(@))]`
`= sin^(-1) (cot (90^(@))) = sin^(-1) (0) = 0`