Let `a = cos^(-1) cos 20, b = cos^(-1) cos 30 and c = sin^(-1) sin (a + b)` then
If `5 sec^(-1) x + 10 sin^(-1) y = 10 (a + b + c)` then the value of `tan^(-1) x + cos^(-1) (y -1)` is

Options

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

Answer

B

Explanation

`5 sec^(-1) x + 10 sin^(-1) y = 10 pi`
`rArr sec^(-1) x = pi and sin^(-1) y = (pi)/(2)`
`rArr x = - 1, y = 1`
So, `tan^(-1) (-1) + cos^(-1)(0) = -(pi)/(4) + (pi)/(2) = (pi)/(4)`