Prove that: (sin 3x + sin x) sin x + (cos 3x – cos x) cos x = 0

Asked by Pragya Singh | 1 year ago |  105

##### Solution :-

Consider

LHS = (sin 3x + sin x) sin x + (cos 3x – cos x) cos x

By further calculation

= sin 3x sin x + sin2 x + cos 3x cos x – cos2 x

Taking out the common terms

= cos 3x cos x + sin 3x sin x – (cos2 x – sin2 x)

Using the formula

cos (A – B) = cos A cos B + sin A sin B

= cos (3x – x) – cos 2x

So we get

= cos 2x – cos 2x

= 0

= RHS

Answered by Abhisek | 1 year ago

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