Question

Cos7x+cos5x/sin7x-sin5x = cots/2-cosecx

Answer 1

Answer:

Formulas:

cos x + cos y = 2 cos ((x + y) / 2) cos ((x - y) / 2)

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

So cos 7x + cos 5x = 2 cos 6x cos x and sin 7x - sin 5x = 2 sin x cos 6x

(cos 7x + cos 5x) / (sin 7x - sin 5x) = 2 cos 6x cos x / 2 sin x cos 6x = cos x / sin x = cot x