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Question
Prove the following :
sin 6x + sin 4x – sin 2x = 4 cos x sin 2x cos 3x
Solution
L.H.S. = sin 6x + sin 4x – sin 2x
= `2sin((6x + 4x)/2) cos((6x - 4x)/2) - 2sinx cosx`
= 2 sin 5x cos x – 2 sin x cos x
= 2 cos (sin 5x – sin x)
= `2cosx [2cos((5x + x)/2)sin((5x - x)/2)]`
= 2 cos x (2 cos 3x sin 2x)
= 4 cos x sin 2x cos 3x
= R.H.S.
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