SOLUTION: I need help verifying this identity, factoring is confusing me. Shouldn't I begin by factoring the top on the left side? cos 5x cos 3x + sin 5X sin 3x CSC X ---------

Algebra ->  Trigonometry-basics -> SOLUTION: I need help verifying this identity, factoring is confusing me. Shouldn't I begin by factoring the top on the left side? cos 5x cos 3x + sin 5X sin 3x CSC X ---------      Log On


   

Question 132787: I need help verifying this identity, factoring is confusing me. Shouldn't I begin by factoring the top on the left side?

cos 5x cos 3x + sin 5X sin 3x CSC X
----------------------------- = -------
sin 3x - sin X 2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Note: I'm only manipulating the left side. I'm showing the right just for comparison.




Start with the given equation




Condense the numerator by using the identity cos%28x-y%29=cos%28x%29cos%28y%29%2Bsin%28x%29sin%28y%29



Combine like terms




Use the identity to replace the numerator



Expand 3x to 2x+x


Expand sin%282x%2Bx%29 through this identity


Replace sin%282x%29 with the identity


Multiply




Replace with



Distribute


Replace with



Distribute



Combine like terms




Factor out the GCF



Cancel like terms






Simplify



replace 1%2Fsin%28x%29 with csc%28x%29