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. $
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. $
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.