if `cos^(- 1)sqrt(p)+cos^(- 1)sqrt(1-p)+cos^(- 1)sqrt(1-q)=(3pi)/4` ,then the value of q is (A) 1 (B) `1/sqrt(2)` (C) `1/3` (D) `1/2`

Options

A. 1
B. `(1)/(sqrt2)`
C. `(1)/(3)`
D. `(1)/(2)`

Answer

D

Explanation

`cos^(-1) sqrtp + cos^(-1) sqrt(1 - p) + cos^(-1) sqrt(1 -q) = (3pi)/(4)`
or `cos^(-1) sqrtp + cos^(-1) sqrt(1 -(sqrtp)^(2)) + cos^(-1) sqrt(1 -q) = (3pi)/(4)`
or `cos^(-1) sqrtp + sin^(-1) sqrtp + cos^(-1) sqrt(1 -q) = (3pi)/(4)`
or `(pi)/(2) + cos^(-1) sqrt(1 -q) = (3pi)/(4)`
or `cos^(-1) sqrt(1 -q) = (3pi)/(4) - (pi)/(2)`
or `cos^(-1) sqrt(1 -q) = (pi)/(4)`
or `sqrt(1-q) = (pi)/(4)`
or `sqrt(1 -q) = cos.(pi)/(4)`
or `sqrt(1 -q) = (1)/(sqrt2)`
or `q = (1)/(2)`