Question

cos3x sin 9x - sin x cos 5x/cos x cos5x-sin 3x sin 9x=tan8x​

Answer 1

Answer:

sin A+sin B=2 sin(A+B/2).cos(A-B/2)

cos A+cos B=2 cos(A+B/2).cos(A-B/2)

cos A-cos B=-2 sin(A+B/2).sin(A-B/2)

(sin 7 x+sin x-(sin 5 x+sin 3 x)/(cos 7 x+cos 3 x -(cos 5 x+cos x)

(2 sin 4 x.cos 3 x-2 sin 4 x.cos x)/(2 cos 5 x.cos 2 x-2 cos 3 x.cos 2 x)

{2 sin 4 x(cos 3 x-cos x)}/{2 cos 2 x(cos 5 x-cos 3 x)

{2 sin 4 x(-2 sin 2 x.sin x)}/{2 cos 2 x(-2 sin 4 x.sin x)}

(-4 sin x.sin 2 x.sin 4 x)/(-4 sin x.cos 2 x .sin 4 x)

sin 2 x/cos 2 x

tan 2 x