From: Courtney

I am trying to solve the problem:

Show that this equation is an identity:
(sin x + sin 2X)/(cos x - cos 2x) = cot(x/2)

I have tried to solve it, and I've gotten it broken down to
(sinx(1+2cosx))/(cosx-1)

Where do I go from there to get to the answer that I need?

Hi Courtney.

I see that in the numerator, you have used the known identity sin 2x = 2(sin x)(cos x), but the denominator you've written doesn't make sense to me because cos x - cos 2x can't equal cosx - 1 (otherwise cos 2x would always equal 1!)

Here's how I would prove it:

Hope this helps,
Stephen La Rocque.