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` is (a)`[-1,1]-{0}` (b) `(0,1)uu{-1}` (c)`[-1,0)uu{1}` (d) `[-1,1]`

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}`