trig function expressions?

Question

Simplify the expression.
tan(sin-1(x))

Answer 1

Remember that according to definition, sin-1(x) is in the range -pi/2 to pi/2.
You may let sin-1(x) = t, thus sin t = x
So cos t = sqrt(1 - x^2)
tan(sin-1(x)) = tan t = x/sqrt(1 - x^2)