SOLUTION: 2(sin(x))^2-3cos(x)+3=0 what is the exact answer

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Question 584497: 2(sin(x))^2-3cos(x)+3=0 what is the exact answer
Answer by lwsshak3(11628) About Me  (Show Source):
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2(sin(x))^2-3cos(x)+3=0 what is the exact answer
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2(sin(x))^2-3cos(x)+3=0
2(1-cos^2x)-3cosx+3=0
2-2cos^2x-3cosx+3=0
-2cos^2x-3cosx+5=0
2cos^2x+3cosx-5=0
(2cosx+5)(cosx-1)=0
..
2cosx+5=0
cosx=-5/2 (reject, cosx>-1)
..
cosx-1=0
cosx=1
x=0