Question 2:
Prove that: (sin 3x + sin x) sin x + (cos 3x − cos x) cos x = 0
Answer
L.H.S. = (sin 3x + sin x) sin x + (cos 3x − cos x) cos x = 0
=sin 3x sin x + sin2 x + cos 3x cos x – cos2 x
=cos 3x cos x + sin 3x sin x – (cos2x – sin2 x)
= cos(3x – x) – cos 2x [cos(A – B) = cos A cos B + sin A sin B]
=cos 2x – cos 2x
= 0
= R.H.S.
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