Question:
Sin3x sin2x-sinx=4sinx cosx/2 cos3x/2,prove?
Answer:
Given sin 3x + sin 2x - sin x
= sin 3x - sin x + sin 2x
= 2 * cos(3x + x)/2 * sin(3x - x)/2 + sin 2x
= 2 * cos 2x * sin x + 2 * sin x * cos x (sin 2x = 2*sin x * cos x)
= 2 * sin x * (cos 2x + cos x)
= 2 * sin x * 2 * cos(2x + x)/2 * cos(2x - x)/2
= 4 * sin x * cos(3x/2) * cos(x/2)
So, sin 3x + sin 2x - sin x = 4 * sin x * cos(x/2) * cos(3x/2)
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