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Question
Prove the following:
cot 4x (sin 5x + sin 3x) = cot x (sin 5x – sin 3x)
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Solution
L.H.S. = cot 4x (sin 5x + sin 3x)
= cot 4x × 2sin `(5x + 3x)/2 cos (5x - 3x)/2`
[∵ sin C + sinD = 2sin `(C + D)/2 cos (C - D)/2`]
= 2 `(cos4x)/(sin4x) sin 4x cos x`
= 2 cos 4x cos x
R.H.S. = cot x (sin 5x - sin 3x)
= `(cosx)/(sinx) xx 2 sin x cos 4x`
= 2 cos x cos 4x
Hence L.H.S. = R.H.S.
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