SOLUTION: Could you please help me solve this equation over 1 rotation? 2sinX - 1 = cscX Thank you very much

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Question 329125: Could you please help me solve this equation over 1 rotation?
2sinX - 1 = cscX
Thank you very much
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
2sin%28x%29-1=1%2Fsin%28x%29
2%28sin%28x%29%29%5E2-sin%28x%29=1
Substitute S=sin%28x%29
2S%5E2-S-1=0
%282S%2B1%29%28S-1%29=0
Two solutions:
2S%2B1=0
2S=-1
S=-1%2F2
sin%28x%29=-1%2F2
x=7pi%2F6 and x=11pi%2F6
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S-1=0
S=1
sin%28x%29=1
x=pi%2F2
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Three solutions in total:
x=pi,x=7pi%2F6,x=11pi%2F6
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Graph of f%28x%29=2sin%28x%29-1-csc%28x%29 showing the 3 zeros.
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