Expert: Paul Klarreich - 2/26/2009

Question
cos 5x cos 3x + sin 5x sin 3x / sin 3x - sin x = csc x / 2

Answer
Questioner:   Philli
Category:  Calculus
Private:  No
 
Subject:  Identities
Question:  cos 5x cos 3x + sin 5x sin 3x / sin 3x - sin x = csc x / 2

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I am not sure what that says, because you didn't parenthesize properly, I believe.  But here is an idea:

cos A cos B + sin A sin B is the right side of a standard identity.  Look it up and apply it to the top of your:

cos 5x cos 3x + sin 5x sin 3x
-----------------------------  
   sin 3x - sin x


Now look up something called "Sum-to-product Formulas" and apply one of them to the bottom of that.  If you do that, you will be OK.

If you are still stuck, let me know.