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

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

Answers

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

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

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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