SOLUTION: find all solutions on the interval 0 ≤x≤2pi : sin^(2)x-3cos^(2)x=0

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Question 445499: find all solutions on the interval 0 ≤x≤2pi : sin^(2)x-3cos^(2)x=0
Answer by Gogonati(855) About Me  (Show Source):
You can put this solution on YOUR website!
%28sinx%292-3%28cosx%29%5E2=0, substitute %28sinx%29%5E2=1-%28cosx%29%5E2, and get:
1-%28cosx%29%5E2-3%28cosx%29%5E2=0 => 4%28cosx%29%5E2=1 => %28cosx%29%5E2=1%2F4.
The last equation is equivalent with two equations:
cosx=1%2F2 and cosx=-1%2F2. The solution for the first equation is:
x=pi%2F3 and x=5pi%2F3. The solution for the second equation is:
x=2pi%2F3 and x=4pi%2F3.