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Prove that sin x + sin 3x + sin 5x + sin 7x = 4cos x . cos 2x . sin 4x

Prove that sin x + sin 3x + sin 5x + sin 7x =  4cos x .  cos 2x . sin 4x

Grade:11

1 Answers

Shashank Singh
askIITians Faculty 57 Points
3 years ago
use sinC +sinD seperately for sinx+sin7x and sin3x +sin5x
we will get,
2sin4xcos3x+2sin4xcosx
= 2sin4x(cos3x+cosx)
= 2sin4x(2cos2xcosx)
= 4cosxcos2xsin4x...... [ans]

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