Question

prove it
i want it fast because tomorrow my exam

Answer 1

Numerator:

We know that sin a - sin b = 2 cos(a+b/2) sin(a-b/2)

sin x - sin 3x = 2 cos(x+3x/2) sin(x-3x/2)

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

                     = 2 cos 2x sin (-x).   ------ (1)


Denominator:

We know that cos^2x-sin^2x = cos 2x.

Given sin^2 x - cos^2x = -cos2x.    ---------- (2)


On solving (1) and (2), we get

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

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

= 2 sin x.


Hope this helps!