Solving Trig Equations: Tips and Tricks for Finding Solutions

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The discussion revolves around solving a trigonometric equation, specifically Sin(θ) = (1/2)(1/Cos(θ) + Cos(θ)). Initially, the poster struggled with the equation but managed to find a solution shortly after posting. They acknowledged a previous manipulation error that hindered their progress. Another participant expressed ongoing difficulty in solving the same equation. The conversation highlights common challenges in manipulating trigonometric functions and the importance of careful algebraic manipulation.
jamjar
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Hi,
I'm trying to solve this trig equation. I've tried representing everything in terms of sin or cos but I don't ever seem to get anywhere useful.
Any pointers?

Sin(\theta ) = \frac{1}{2}\left( {\frac{1}{{Cos(\theta )}} + Cos(\theta )} \right)<br />
 
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Well, I just solved that anyway, 1 minute after posting it.
I had some wacky manipulation error before that I spotted.
 
How did you solve it? I have been studying this problem and I cannot find a solution.
 

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