Question

Prove the following :

sin 6x + sin 4x – sin 2x = 4 cos x sin 2x cos 3x

Answer 1

L.H.S. = sin 6x + sin 4x – sin 2x

= `2sin((6x + 4x)/2) cos((6x - 4x)/2) - 2sinx cosx`

= 2 sin 5x cos x – 2 sin x cos x

= 2 cos (sin 5x – sin x)

= `2cosx [2cos((5x + x)/2)sin((5x - x)/2)]`

= 2 cos x (2 cos 3x sin 2x)

= 4 cos x sin 2x cos 3x

= R.H.S.