SOLUTION: How to solve 3 sec^2 theta + 5 sec theta + 2 = 0?

Question 757215: How to solve 3 sec^2 theta + 5 sec theta + 2 = 0?

Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
How to solve 3 sec^2 theta + 5 sec theta + 2 = 0?
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For simplicity, I will replace theta with x.
Since sec x = 1/cos x we can write
3/cos^2(x) + 5/cos(x) + 2 = 0
Multiply through by cos^2(x):
2cos^2(x) + 5cos(x) + 3 = 0
This can be factored as
(2cos(x)+3)(cos(x)+1) = 0
The solutions are cos(x) = -1 and cos(x) = -3/2
Since the magnitude of cos(x) can not be > 1, we discard the 2nd solution.
This gives x = n* where n=integer

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