The solution set of the equation
`sin^(-1) sqrt(1 - x^(2)) + cos^(-1) x = cot^(-1) ( sqrt(1-x^(2))/x) - sin^(-1) x `

Options

A. `[-1, 1] -{0}`
B. `(0, 1] uu {-1}`
C. `[-1, 0) uu {1}`
D. `[-1, 1]`

Answer

C

Explanation

`sin^(-1). sqrt(1 -x^(2)) + cos^(-1) x = cot^(-1). (sqrt(1-x^(2)))/(x) - sin^(-1)x`
or `(pi)/(2) + sin^(-1). sqrt(1 -x^(2)) = cot^(-1). (sqrt(1-x^(2)))/(x)`
`tan^(-1). (sqrt(1 -x^(2)))/(x) = - sin^(-1) sqrt(1 -x^(2))`
`rArr x in [-1, 0) uu {1}`