SOLUTION: prove that 2 cos square theta+3 sin theta=0

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Question 963442: prove that 2 cos square theta+3 sin theta=0
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
You can't prove it because it's not an identity.
You need to solve the equation for the values of theta for which this equation holds.
2cos%5E2%28theta%29%2B3sin%28theta%29=0
2%281-sin%5E2%28theta%29%29%2B3sin%28theta%29=0
-2sin%5E2%28theta%29%2B3sin%28theta%29%2B2=0
2sin%5E2%28theta%29-3sin%28theta%29-2=0
Substitute, u=sin%28theta%29
2u%5E2-3u-2=0
%28u-2%29%282u%2B1%29=0
Two solutions:
u-2=0
u=2
sin%28theta%29=2
No solution exists.
.
.
2u%2B1=0
2u=-1
u=-1%2F2
sin%28theta%29=-1%2F2
theta=210 and theta=330