SOLUTION: Prove the following identity (2tanx-sin2x)/(2sin^2×)=tanx

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Question 1179268: Prove the following identity

(2tanx-sin2x)/(2sin^2×)=tanx


Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


%282tan%28x%29-sin%282x%29%29%2F%282sin%28x%29%5E2%29

Unless you have a huge amount of experience with solving trig identities, change everything to sines and cosines. And of course use the double angle formula to replace sin(2x).

%282%28sin%28x%29%2Fcos%28x%29%29-%282sin%28x%29cos%28x%29%29%29%2F%282sin%28x%29%5E2%29

You won't learn much from this if I finish the problem for you....

Here is what you need to do from here:
(1) combine the expressions in the numerator using the least common denominator, cos(x);
(2) rewrite the expression (a fraction within a fraction) as a single fraction;
(3) factor the numerator;
(4) use the identity sin%28x%29%5E2%2Bcos%28x%29%5E2=1 to rewrite the fraction;
(5) simplify the fraction;
(6) verify that what you have left is equal to tan(x)