I need to prove this identity for homework and I can't figure it out.
asked Apr 14, 2013 in Trigonometry Answers by anonymous

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:

To avoid this verification in future, please log in or register.

1 Answer

The question should be:

prove (cos(3x)-cos(7x))/(sin(3x)+sin(7x))=tan(2x).



So, cos(A-B)-cos(A+B)=2sinAsinB and


Also, sin(A+B)=sinAcosB+cosAsinB and

sin(A-B)=sinAcosB-cosAsinB, so



If A-B=3x and A+B=7x, 2A=10x, A=5x and B=2x.

Therefore, cos(3x)-cos(7x)=2sin(5x)sin(2x) and

sin(3x)+cos(7x)=2sin5xcos(2x) and


2sin(5x)sin(2x)/(2sin(5x)cos(2x))=tan(2x) QED

answered Nov 28, 2016 by Rod Top Rated User (429,080 points)
Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
78,069 questions
81,863 answers
61,225 users