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