Precalculus math help

Question

Prove the following identity. Show all work.

Answer 1

cotx = cosx/sinx

sin2x = 2cosxsinx

cos2x = cos^2x - sin^2 = 1-sin^2x -sin^2x = 1-2sin^2x

cos2x + sin^2x = 1

cos2x = 1-sin^2x

1-cos2x = 1 - 1 + 2sin^2x = 2sin^2x

sin2x/(1-cos2x) = 2cosxsinx/2sin^2x = cosx/sinx = cotx

Answer 2

sin 2θ / (1 - cos 2θ)

(2 sin θ cos θ) / (1 - (1 - sin² θ)

(2 sin θ cos θ) / sin² θ

2 cos θ / sin θ

2 cot θ