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Prove that (sin 3 x+sin x) sin x+(cos 3 ...

Prove that `(sin 3 x+sin x) sin x+(cos 3 x-cos x)cosx=0`

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L.H.S .=[2 sin ((3 x+(x))/(2)) cos ((3 x-x)/(2))] sin x+[-2 sin ((3 x+x)/(2 !)) sin ((3 x-x)/(2))] cos x.
.=2 sin 2 x cos x sin x-2 sin 2 x sin x cos x=0=. R.H.S
.therefore. L.H:S .=. R.H.S
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