SOLUTION: solve the equation on the interval (0,2pi) tan (x/3) = root 3

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Question 358878: solve the equation on the interval (0,2pi)
tan (x/3) = root 3
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
tan+%28x%2F3%29+=+sqrt%283%29,
%28tan+%28x%2F3%29%29%5E2+=+3,after both sides.
1%2B%28tan+%28x%2F3%29%29%5E2+=+4,
%28sec+%28x%2F3%29%29%5E2+=+4, by a Pythagorean identity.
%28cos%28x%2F3%29%29%5E2+=+1%2F4, after taking reciprocals.
cos%28x%2F3%29+=+1%2F2 orcos%28x%2F3%29+=-+1%2F2.
The first equation gives x%2F3+=+pi%2F3, the second x%2F3+=+%284%2Api%29%2F3.
further simplification gives x+=+pi and x+=+4%2Api. The second answer is not acceptable, therefore the final answer is x+=+pi.