Question

МАТ ПРОФ 13 ЗАДАНИЕ​

Answer 1

a)

$\sqrt{3}\cos(x)+2cos(x-\frac{5\pi}{6})=\cos(2x)\\\sqrt{3}\cos(x)+2(\cos(x)cos(\frac{5\pi}{6})+\sin(x)\sin(\frac{5\pi}{6}))=\cos(2x)\\\sqrt{3}\cos(x)+2(-\frac{\sqrt{3}}{2}\cos(x)+\frac{1}{2}\sin(x))=cos(2x)\\\sqrt{3}\cos(x)-\sqrt{3}cos(x)+\sin(x)=cos(2x)\\\sin(x)=cos(2x)\\\sin(x)=1-2\sin^2(x)\\2\sin^2(x)+\sin(x)-1=0\\D=1+8=9\\\sin(x)=\frac{1}{2};-1\\x=\frac{\pi}{6}+2\pi k\\x=\frac{5\pi}{6}+2\pi k\\x=\frac{3\pi}{2}+2\pi k$

б)

$-\frac{9\pi}{2};-\frac{31}{6}$