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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