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

Asked by Gowtham (student) , on 13/10/12

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(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

Posted by pallintimanish... (student) on 14/10/12

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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

Posted by Hari Govind (student) on 22/5/14

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