SOLUTION: find all solutions of the equation in the interval [0,2pie) 2 sin x + csc x = 0 2 sec^2 x + tan^2 x - 3 = 0

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Question 924600: find all solutions of the equation in the interval [0,2pie)
2 sin x + csc x = 0
2 sec^2 x + tan^2 x - 3 = 0

Found 2 solutions by Alan3354, lwsshak3:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
It's the Greek letter pi, not the dessert, pie.

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
find all solutions of the equation in the interval [0,2pie)
2 sin x + csc x = 0
2 sec^2 x + tan^2 x - 3 = 0
***
2sinx%2Bcscx=0
2sinx%2B1%2Fsinx=0
2sin%5E2%28x%29%2B1=0
sin%5E2%28x%29=-1%2F2
no solution
..
2sec%5E2%28x%29%2Btan%5E2%28x%29-3=0
2%2Fcos%5E2%28x%29%2Bsin%5E2%28x%29%2Fcos%5E2%28x%29-3=0
2%2Bsin%5E2%28x%29-3cos%5E2%28x%29=0
2%2B1-cos%5E2%28x%29-3cos%5E2%28x%29=0
3-4cos%5E2%28x%29=0
4cos^2(x)=3
cos^2(x)=3/4
cos(x)=±√3/2
x=π/6,5π/6,7π/6,11π/6