Verify: sin9x+sin5x/cos9x-cos5x=cot2x

Question

This is for my trig class, thanks for the help!

Answer 1

(sin9x+sin5x)/(cos9x-cos5x)

= (sin(7x+2x) + sin(7x-2x))/(cos(7x+2x)-cos(7x-2x))

= 2sin7x cos2x / (2sin7x sin 2x)

= cot2x