SOLUTION: Prove the identity. 5tan(3x) = (15tan(x) − 5tan^3(x))/ (1 − 3tan^2(x))

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Question 1157401: Prove the identity.
5tan(3x) = (15tan(x) − 5tan^3(x))/ (1 − 3tan^2(x))
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
5tan%283x%29+=+%2815tan%28x%29+-+5tan%5E3%28x%29%29%2F+%281+-+3tan%5E2%28x%29%29

We will work only with the left side.  We will use this formulas:

                

               and its corollary:

               tan%5E%22%22%282theta%29=%282tan%5E%22%22%28theta%29%29%2F%281-tan%5E2%28theta%29%29 




Distribute the 5 to remove parentheses on the top and
multiply tangents on the bottom:





Distribute to remove the parentheses:



Combine terms:

%2815tan%28x%29+-+5tan%5E3%28x%29%29%2F+%281+-+3tan%5E2%28x%29%29

Edwin