Please, simplify these trigonometry term: \frac{\sin 2x+\sin 4x+\sin 6x}{\cos 2x+\cos 4x+\cos

Dashawn Robbins

Dashawn Robbins

Answered question

2022-04-28

Please, simplify these trigonometry term:
sin2x+sin4x+sin6xcos2x+cos4x+cos6x=?

Answer & Explanation

Davon Friedman

Davon Friedman

Beginner2022-04-29Added 13 answers

As the angles are in Arithmetic Progression,
sin2x+sin4x+sin6x=2sinx(sin2x+sin4x+sin6x)2sinx
=cosxcos7x2sinx
Now as cosCcosD=2sinC+D2sinDC2
cosxcos7x=2sin4xsin3x
Similiarly, cos2x+cos4x+cos6x=sin7xsinx2sinx
Now as sinCsinD=2sinCD2cosC+D2, sin7xsinx=2sin3xcos4x

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