Solve \sin 7x+\sin 3x=0

Jakayla Benton

Jakayla Benton

Answered question

2022-04-19

Solve sin7x+sin3x=0

Answer & Explanation

2sze1c1se3nh

2sze1c1se3nh

Beginner2022-04-20Added 17 answers

Hint: by addition formulas you have
sin(5x+2x)=sin5xcos2x+cos5xsin2x
sin(5x-2x)=sin5xcos2x-cos5xsin2x so if you add the two equations you end up withsin(5x+2x)+sin(5x-2x)=2sin5xcos2x

Yaretzi Odom

Yaretzi Odom

Beginner2022-04-21Added 16 answers

Hint:
Use Prosthaphaeresis Formulas
and siny=0y=mπ
and cosz=0z=(2r+1)π2
or
sin7xsin3x=sin(3x)7x=nπ+(1)n(3x)
where m,n,r are arbitrary integers

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