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Question

Prove that:

sin 3x+ sin 2x - sin x = 4 sin x cosx2cos3x2

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Solution

We have L.H.S

= sin 3x + sin 2x - sin x.

= (sin 3x - sin x) + sin 2x

= [2 cos(3x+x2)sin(3xx2)]+2 sin x cos x[sin C- sin D = 2 cosC+D2sinCD2]

= 2 cos 2x sin x + 2 sin x cos x

= 2 sin x [ cos 2x+ cos x]

= 2 sin x [2 cos(2x+x2)cos(2xx2)]

= 2 sin x [2 cos(3x2)cos(x2)]

= 4 sin x cos x2 cos 3x2 = R.H.S.


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