Question

Sin πx/6 -√3 cos πx/6 =2 ответ -7​

Answer 1

Ответ:   $x=5+12n\; ,\; \; n\in Z$ .

Объяснение:

$sin\frac{\pi x}{6}-\sqrt3\, cos\frac{\pi x}{6}=2\; |:2\\\\\frac{1}{2}\, sin\frac{\pi x}{6}-\frac{\sqrt3}{2}\, cos\frac{\pi x}{6}=1\\\\cos\frac{\pi}{3}\cdot sin\frac{\pi x}{6}-cos\frac{\pi }{3}\cdot cos\frac{\pi x}{6}=1\\\\sin(\frac{\pi x}{6}-\frac{\pi}{3})=1\\\\\frac{\pi x}{6}-\frac{\pi}{3}=\frac{\pi}{2}+2\pi n\; ,\; n\in Z\\\\\frac{\pi x}{6}=\frac{5\pi }{6}+2\pi n\; ,\; n\in Z\\\\x=5+12n\; ,\; \; n\in Z$