Question:
(sin 3x + sin x) sin x + (cos 3x - cos x) cos x = 0
Answer:
Given
(sin 3x + sin x) sin x + (cos 3x - cos x) cos x
= {2*sin(3x+x)/2 * cos(3x-x)/2}sinx + {-2*sin(3x+x)/2 * sin(3x-x)/2}*cosx
= 2*sin2x*cosx*sinx - 2*sin2x*sinx*cosx
= 0
So (sin 3x + sin x) sin x + (cos 3x - cos x) cos x = 0
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