The number of solutions of the equation `cos^(-1)((1+x^2)/(2x))-cos^(-1)x=pi/2+sin^(-1)x` is 0 (b) 1 (c) 2 (d) 3

Options

A. 0
B. 1
C. 2
D. 3

Answer

B

Explanation

`cos^(-1) ((1 + x^(2))/(2x)) = (pi)/(2) + (sin^(-1) x + cos^(-1) x)`
`rArr cos^(-1) ((1 + x^(2))/(2x)) = pi`
or `((1 + x^(2))/(2x)) = cos pi = -1`
or `x^(2) + 1 + 2x = 0`
or `x = -1`