help with precal!?

Question

Discuss how to prove the identity:


tan(sin^-1(k))=k/rad(1-k^2)

Answer 1

if the side of a triangle with sine(theta) = k then the opposite side is k and the hypotenuse is 1, which makes the adjacent side = sqrt(1-k^2)
so sin^-1(k)=theta and
tan(theta)= opposite/adjacent = k/sqrt(1-k^2)

Answer 2

To do that one I'd begin by drawing a right triangle with a hypotenuse of 1 and a short side of k. Then the angle in the reference position is sin^(-1) k and the long side is sqrt (1-k^2). Then by definition of tangent the tangent of the angle in reference position is k/(sqrt (1- k^2)) which I hope / assume is what you mean by rad(1 - k^2)