Question

2sin(x+ п/4)=корень из 2

Answer 1

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