Question

2sin(1x/3-П/3)= корень из 3

Answer 1

$2\sin( \frac{x}{3} - \frac{\pi}{3} )= \sqrt{3}$

$\sin( \frac{x}{3} - \frac{\pi}{3} )= \frac{\sqrt{3}}{2}$

$\frac{x}{3} - \frac{\pi}{3}= (-1)^k \frac{\pi}{3} +k\pi,\quad k\in Z$

$\frac{x}{3} = (-1)^k \frac{\pi}{3} +\frac{\pi}{3}+k\pi,\quad k\in Z$

Умножим обе части на 3

$x = (-1)^k \pi +\pi+3k\pi,\quad k\in Z$

$x = \pi*(1+3k+(-1)^k),\quad k\in Z$