If `-1 lt x lt 0` then `sin^(-1) x` equals-

Options

A. `pi- cos^(-1) (sqrt(1-x^(2)))`
B. `tan^(-1) ((x)/(sqrt(1-x^(2))))`
C. `-cos^(-1)((sqrt(1-x^(2)))/(x))`
D. `cosec^(-1)x`

Answer

B

Explanation

`:' -1 lt x lt 0`,
then `- (pi)/(2) lt sin^(-1) x lt 0`
Let `sin^(-1) x = alpha`
`:. Sin alpha = x`
then, ` tan alpha = ((x)/(sqrt(1-x^(2))))`
`:.alpha = tan^(-1)((x)/(sqrt(1-x^(2))))`
`:. sin^(-1)x = tan^(-1)((x)/(sqrt(1-x)^(2)))`