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Question
Prove the following:
(sin 3x + sin x)sin x + (cos 3x – cos x) cos x = 0
Solution
L.H.S. = (sin 3x + sin x)sin x + (cos 3x – cos x) cos x
= sin 3x sin x + sin2x + cos 3x cos x – cos2x
= (cos 3x cos x + sin 3x sin x) – (cos2x – sin2x)
= cos (3x – x) – cos 2x
= cos 2x – cos 2x
= 0
= R.H.S.
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