Verify: (1+cos(2theta))/(sin(2theta)) = cot(theta)

Question

I could not get them to equal each other, but I may have been going about it the wrong way

Answer 1

(1+cos(2Θ))/sin(2Θ) = cotΘ

1 + cos(2Θ) = 1 + Cos(Θ+Θ) = 1 + cos²Θ - sin²Θ = 1 + cos²Θ - (1 - cos²Θ) = 2cos²Θ

and sin(2Θ) = 2sinΘ*cosΘ

hence (1 + cos(2Θ) )/sin(2Θ) = 2cos²Θ / (2sinΘ*cosΘ) = cosΘ / sinΘ = cotΘ