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Gowtham , asked a question
Subject: Math , asked on 13/10/12

prove that sin x+sin3x+sin5x+sin7x=4cosx cos2x sin 4x

pallintimanish... , added an answer, on 14/10/12
5 helpful votes in Math

 sinx+sin3x+sin5x+sin7x

(sin 3x +  sin 5x)  +  (sin 7x  +  sin x )

2 sin 4x . cos x +  2 sin 4x . cos 3x

2 sin 4x (cos x+ cos 3x)

2 sin 4x (2 cos 2x . cos x)

2 cos 2x . cos x . sin 4x

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Diksha Parewa , added an answer, 3 weeks, 4 days ago
6 helpful votes in Math
We first need to arrange numbers so that there sum can be easily divisible by 2 .

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Tanmay , added an answer, 1 week, 6 days ago
1 helpful votes in Math
= sin x+sin 3x+sin 5x+sin 7x = (sinx+sin 7x)+(sin 5x+sin 3x) =2 sin 4x.cos x+sin 4x.cos 3x =2 sin 4x[cos 3x+cos x] =2 sin 4x[2 cos 2x+cos x] =4 sin 4x.cos2x+cos x
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Hari Govind , added an answer, on 22/5/14

LHS= sin x+sin 3x+sin 5x+sin 7x = (sinx+sin 7x)+(sin 5x+sin 3x) =2 sin 4x.cos x+sin 4x.cos 3x =2 sin 4x[cos 3x+cos x] =2 sin 4x[2 cos 2x+cos x] =4 sin 4x.cos2x+cos x hence proved

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