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

**Solution:**

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

= sin 3x sin x + sin^{2}x + cos 3x cos x - cos^{2}x

= cos 3x cos x + sin 3x sin x - (cos^{2}x - sin^{2}x)

= cos (3x - x) - cos 2x [Because cos (A - B) = cos A cos B + sin A sin B and cos 2A = cos^{2}A - sin^{2}A]

= cos 2x - cos 2x

= 0

= RHS

NCERT Solutions Class 11 Maths Chapter 3 Exercise ME Question 2

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

**Summary:**

We got, (sin 3x + sin x)sin x + (cos 3x - cos x)cos x = 0. Hence Proved

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