Question

2 cos (x/2 + п/4) + 1 = 0

Answer 1

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