SOLUTION: Solve for cot^2 theta + 3/sintheta + 3=0

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Question 922673: Solve for cot^2 theta + 3/sintheta + 3=0
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x, cot^2 theta + 3/sintheta + 3=0 For interval[0,2π)
cot%5E2%28x%29%2B3%2Fsinx%2B3=0
cos%5E2%28x%29%2Fsin%5E2%28x%29%2B3%2Fsinx%2B3=0
lcd:sin^2(x)
cos%5E2%28x%29%2B3sinx%2B3sin%5E2%28x%29=0
1-sin%5E2%28x%29%2B3sinx%2B3sin%5E2%28x%29=0
2sin%5E2%28x%29%2B3sinx%2B1=0
(2sinx+1)(sinx+1)=0
sinx=-1/2
x=7π/6, 11π/6 (In quadrants III and IV where sin<0)
or
sinx=-1
x=3π/2