2sin x/4=✓2 2cos x/4=✓2​

Решите задачу:

$1)2Sin\frac{x}{4}=\sqrt{2} \\\\Sin\frac{x}{4}=\frac{\sqrt{2} }{2}\\\\\frac{x}{4}=(-1)^{n}arcSin\frac{\sqrt{2} }{2}+\pi n,n\in z\\\\\frac{x}{4}=(-1)^{n}\frac{\pi }{4}+\pi n,n\in z\\\\x=(-1)^{n}\pi +4\pi n,n\in z$

$2)2Cos\frac{x}{4}=\sqrt{2}\\\\Cos\frac{x}{4}=\frac{\sqrt{2} }{2}\\\\\frac{x}{4}=\pm arcCos\frac{2}{2}+2\pi n,n\in z\\\\\frac{x}{4} =\pm\frac{\pi }{4}+2\pi n,n\in z\\\\x=\pm\pi+8\pi n,n\in z$

2sin x/4=✓2 2cos x/4=✓2​

2sin x/4=✓2 2cos x/4=✓2