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Verify: sin9x+sin5x/cos9x-cos5x=cot2x

This is for my trig class, thanks for the help!

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Robert J. | Certified High School AP Calculus and Physics TeacherCertified High School AP Calculus and Ph...
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(sin9x+sin5x)/(cos9x-cos5x)
= (sin(7x+2x) + sin(7x-2x))/(cos(7x+2x)-cos(7x-2x))
= 2sin7x cos2x / (2sin7x sin 2x)
= cot2x