SOLUTION: show that (cosa+sina)/(cosa-sina)-(cosa-sina)/(cosa+sina)=2tan2a

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Question 1058160: show that (cosa+sina)/(cosa-sina)-(cosa-sina)/(cosa+sina)=2tan2a
Answer by solve_for_x(190) About Me  (Show Source):
You can put this solution on YOUR website!


Multiplying each term to get a common denominator on the left side gives:





+2%282%28sina%29%28cosa%29%29+%2F+%28%28cosa%29%5E2+-+%28sina%29%5E2%29%29

Dividing both the numerator and the denominator by %28cosa%29%5E2 gives:

+2%2A2%28%28sina%29%2F%28cosa%29%29%2F+%281+-+%28sina%29%5E2%2F%28cosa%29%5E2%29

+2%282tana+%2F+%281+-+%28tana%29%5E2%29%29

But 2tana%2F%281+-+%28tana%29%5E2%29+=+tan2a, so

+2%282tana+%2F+%281+-+%28tana%29%5E2%29%29+=+2tan2a