SOLUTION: Prove that 2tan inverse of 1/3= tan inverse of 3/4

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Question 1062386: Prove that
2tan inverse of 1/3= tan inverse of 3/4
Answer by ikleyn(53955) About Me  (Show Source):
You can put this solution on YOUR website!
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Prove that
2tan inverse of 1/3= tan inverse of 3/4
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They want you to prove 


2%2Aarctan%281%2F3%29 = arctan%283%2F4%29.


Let alpha%29 = arctan%281%2F3%29.


It means that tan%28alpha%29 = 1%2F3.

Then tan%282alpha%29 = %282%2Atan%28alpha%29%29%2F%281-tan%5E2%28alpha%29%29 = %282%2A%281%2F3%29%29%2F%281-%281%2F3%29%5E2%29 = %28%282%2F3%29%29%2F%28%288%2F9%29%29 = %289%2A2%29%2F%283%2A8%29 = 3%2F4.

In other words, 2alpha = arctan%283%2F4%29.


It is precisely what has to be proved.