Question

What is the value of `tan (sin^-1 x)`?

Answer 1

`tan(sin^(-1)(x)) = x/(sqrt(1-x^2)`

Explanation:

If `sin^(-1)(x)=theta`
then
`color(white)("XXX")` based on a unit circle (hypotenuse `= 1`)
`color(white)("XXX")` the side opposite `theta` will have a length of `x`
`color(white)("XXX")`and
`color(white)("XXX")`the adjacent side will have a length of `sqrt(1-x^2)` (based on Pythagorean Theorem)

`tan(sin^(-1)(x)) = tan(theta) = ("opposite")/("adjacent") = x/(sqrt(1-x^2))`