<s>[INST] Solving $\cos(2x+\frac{\pi}{4})= -1/2 $ My suggestion: 
$$\cos\left(2x+\frac{\pi}{4}\right)= -\frac{1}{2}$$
$$ 2x+\frac{\pi}{4} = \frac{2\pi}{3} \pm 2\pi n, n\in\mathbb{Z}$$
$$ x= \frac{\left( \frac{2\pi}{3} - \frac{\pi}{4} \right)}{2} \pm 2\pi n, n\in\mathbb{Z}$$
My answer:
$$ x = \frac{5\pi}{24} \pm 2\pi n, n\in\mathbb{Z} $$
But correct answer is:
$$-\frac{\pi}{8} \pm \frac {\pi}{3} + \pi n $$
What's my mistake?
 [/INST] HINT:
$\dfrac12=\cos\dfrac\pi3\implies-\dfrac12=\cos\left(\pi-\dfrac\pi3\right)$ as $\cos(\pi-u)=-\cos u$
$\implies2x+\dfrac\pi4=2m\pi\pm\dfrac{2\pi}3$ where $m$ is any integer
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