SOLUTION: Use an algebraic method to find the solution for 0<=x<=2pi of the equation 5cot x + 2cosec^2 x = 5

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Question 907463: Use an algebraic method to find the solution for 0<=x<=2pi of the equation 5cot x + 2cosec^2 x = 5
Answer by lwsshak3(11628) About Me  (Show Source):
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Use an algebraic method to find the solution for 0<=x<=2pi of the equation
5cot x + 2cosec^2 x = 5
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5cot%28x%29%2B2csc%5E2%28x%29=5
csc^2(x)=cot(x)+1
5cot%28x%29%2B2%28cot%5E2%28x%29%2B1%29=5
5cot%28x%29%2B2cot%5E2%28x%29%2B2=5
2cot%5E2%28x%29%2B5cot%28x%29-3=0
(cot(x)+3)(2cot(x)-1)=0
cot(x)=-3
(Using inverse tan key of calculator set to radians)
x≈2.82, 5.96 (In quadrants II and IV in which cot<0)
or
cot(x)=1/2
x≈1.11, 4.25 (In quadrants I and III in which cot>0)