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How to solve trigonomtry function involving $\sin x \cos x$ and $\sin 2x$:

$\frac{1}{2} \sin(2x) + \sin(x) + 2 \cos(x) + 2 = 0. $

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    After your several questions in trigonometry, it'd be nice if you showed some self-work, some insights, ideas, effort in solving them.2012-08-17

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Hint:

Using the identity $\sin(2x) = 2 \sin x \cos x$ we have $ \sin x \cos x + \sin x + 2\cos x + 2 = 0$ Factor $ (1 + \cos x) \sin x + 2(1 + \cos x) = 0 \\ (1 + \cos x)(2 + \sin x) = 0 $ So either $1 + \cos x = 0$ or $2 + \sin x = 0.$ Solve for $x$ in each case.

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    here's the link http://math.stackexchange.com/questions/183694/how-to-solve-tan2x-sin4x-0 tq2012-08-17