SOLUTION: how to solve 3cot^2 x-4csc x=1 on the interval 0≤x≤2∏

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Question 457930: how to solve 3cot^2 x-4csc x=1 on the interval 0≤x≤2∏
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
solve 3cot^2 x-4csc x=1 on the interval 0≤x≤2∏
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3(csc^2-1)-4csc = 1
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3csc^2 -4csc -4 = 0
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Factor:
3csc^2-6csc+2csc-4 = 0
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3csc(csc-2)+2(csc-2) = 0
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(csc-2)(3csc+1) = 0
csc(x) = 2 or csc(x) = -1/3
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x = pi/4 or (3/4)pi and csc^(-1/3) does not exist
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Cheers,
Stan H.