тригонометрично уравнение sinx + 3cosx = 2

[moni76076]

sinx+?3cosx=2

[dim]

[tex]sin{x}+\sqrt{3}cos{x}=2[/tex] <=> [tex]\frac{1}{2}sin{x}+\frac{\sqrt{3}}{2}cos{x}=1[/tex] <=> [tex]sin{x}cos{60^\circ }+cos{x}sin{60^\circ }=1[/tex] <=> [tex]sin{(x+\frac{\pi}{3})}=1[/tex] => [tex]x+\frac{\pi}{3}=\frac{\pi}{2}+2k\pi[/tex] <=> [tex]x=\frac{\pi}{6}+2k\pi[/tex]