I am having lots of trouble with this problem I have been stuck forever

Question

cos3x/cosx=1-4sin²x

I have to verify the identity

Answer 1

The numerator of left side

cos 3x

cos (2x + x)

cos 2x cos x - sin 2x sin x

(cos² x - sin² x)(cos x) - (2sin x cos x)(sin x)

Divide through by cos x

cos² x - sin² x - 2 sin² x

1 - sin² x - sin² x - 2 sin² x

1 - 4 sin² x

QED