SOLUTION: 2cos^2x-3sinx-3=0

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Question 1042969: 2cos^2x-3sinx-3=0
Answer by ikleyn(52879) About Me  (Show Source):
You can put this solution on YOUR website!
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2cos^2x-3sinx-3=0
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2cos%5E2%28x%29+-+3sin%28x%29+-+3 = 0.

Substitute  cos%5E2%28x%29 = 1+-+sin%5E2%28x%29  to get the equation uniform for sin(x). You will get

2%2A%281-sin%5E2%28x%29%29+-+3sin%28x%29+-3 = 0,  --->

2-2sin%5E2%28x%29+-+3sin%28x%29+-+3 = 0,

2sin%5E2%28x%29+%2B+3sin%28x%29+%2B1 = 0.

Factor left side

(2sin(x)+1)*(sin(x)+1) = 0.

Then the equation deploys in two separate/independent equations:

1)  2sin(x) + 1 = 0  --->  sin(x) = -1%2F2  --->  x = 5pi%2F4  and/or  x = 7pi%2F4.

2)  sin(x) = -1  --->  x = 3pi%2F2.

Answer.  x = 5pi%2F4  and/or  x = 7pi%2F4  and/or  x = 3pi%2F2.