`tan(cos^-1 x)` is equal to

Options

A. `(sqrt(1-x^(2)))/(x)`
B. `(x)/(1+x^(2))`
C. `(sqrt(1+x^(2)))/(x)`
D. `sqrt(1-x^(2))`

Answer

A

Explanation

Let `cos^(-1)x = theta`

`rArr cos theta = x rArr sin theta = sqrt(1-x^(2))`
`rArr tan theta=(sqrt(1-x^(2)))/(x)and theta = cos^(-1)x`
This can be represented by a triangle with hypotenuous = 1 and sindes x and `sqrt(1-x^(2))`.
`rArr tan(cos^(-1)x)=(sqrt(1-x^(2)))/(x)`