Question

Решите уравнение : (Рис.)

Answer 1

$cos(3\pi +x)-sin(\frac{\pi}{2}-x)=\sqrt2\\\\\{cos(3\pi +x)=cos(2\pi +\pi +x)=cos(\pi +x)=-cosx\\\\sin(\frac{\pi}{2}-x)=cosx\}\; \; \to \\\\-cosx-cosx=\sqrt2\\\\-2cosx=\sqrt2\\\\cosx=-\frac{\sqrt2}{2}\\\\x=\pm(\pi-\frac{\pi}{4})+2\pi n=\pm \frac{3\pi}{4}+2\pi n,\; \; n\in Z$