Question

2 cos (x/2 + п/4) + 1 = 0

Answer 1

$2cos( \frac{x}{2}+\frac{\pi}{4} )+1=0\\\\cos( \frac{x}{2}+\frac{\pi}{4} )=-\frac{1}{2}\\\\ \frac{x}{2}+\frac{\pi}{4}=\pm (\pi -arccos\frac{1}{2})+2\pi n=\pm (\pi -\frac{\pi}{3})+2\pi n,\; n\in Z \\\\ \frac{x}{2}+\frac{\pi }{4} =\pm \frac{2\pi }{3}+2\pi n,\; n\in Z\\\\ \frac{x}{2}=-\frac{\pi }{4} \pm \frac{2\pi}{3} +2\pi n,\; n\in Z\\\\x=-\frac{\pi}{2}\pm \frac{4\pi}{3}+4\pi n,\; n\in Z$