The number of roots of the equation `sin^(-1)x-(1)/(sin^(-1)x)=cos^(-1)x-(1)/(cos^(-1)x)` is

Options

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

Answer

C

Explanation

`sin^(-1) x-(1)/(sin^(-1)x)=cos^(-1)x-(1)/(cos^(-1)x)`
`rArr (sin^(-1)x-cos^(-1)x)((sin^(-1)x.cos^(-1)x+1))/(sin^(-1)x.cos^(-1)x)=0`
`rArr sin^(-1)x=cos^(-1)x` or `sin^(-1)x cos^(-1)x+1=0`
`rArr x=(1)/(sqrt(2))` or `sin^(-1)x((pi)/(2)-sin^(-1)x)+1=0`
`rArr x=(1)/(sqrt(2))` or `sin^(-1)x=((pi)/(2)pm sqrt(((pi^(2))/(4)+4)))/(2)`
`rArr x = (1)/(sqrt(2))` or `sin^(-1)x=(pi)/(4)-sqrt((1+(pi^(2))/(16)))`