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 + sin²x + cos 3x cos x - cos²x

= cos 3x cos x + sin 3x sin x - (cos²x - sin²x)

= cos (3x - x) - cos 2x [Because cos (A - B) = cos A cos B + sin A sin B and cos 2A = cos²A - sin²A]

= 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