Question

Решите уравнение:
2 cos (п/4 - x/2) = 1

Answer 1

$2 cos (frac{pi}{4} - frac{x}{2}) = 1\cos(frac{x}{2}-frac{pi}{4})=-frac{1}{2}\frac{x}{2}-frac{pi}{4}=pm(pi-arccosfrac{1}{2})+2pi n\frac{x}{2}-frac{pi}{4}=pm(pi-frac{pi}{3})+2pi n\frac{x}{2}-frac{pi}{4}=pm frac{2pi}{3}+2pi n\frac{x}{2}=pm frac{2pi}{3}+frac{pi}{4}+2pi n\x=pmfrac{4pi}{3}+frac{pi}{2}+4pi n, ; nin Z;\\x_1=frac{11pi}{6}+4pi n, ; nin Z;\x_2=-frac{5pi}{6}+4pi n, ; nin Z.$