1.

Prove the following: sin 6x + sin 4x – sin 2x = 4 cos x sin 2x cos 3x

Answer»

= 2sin (\(\frac{6x+4x}{2}\)) cos (\(\frac{6x-4x}{2}\)) – 2 sin x cos x

= 2 sin 5x cos x — 2 sin x cos x

= 2 cos x (sin 5x — sin x)

= 2 cos[2 cos(\(\frac{5x+x}{2}\)) sin (\(\frac{5x-x}{2}\))]

= 2 cos x (2 cos 3x sin 2x) 

= 4 cos x sin 2x cos 3x 

= R.H.S.



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