Question

√(3)/2×sin(x)-1/2×cos(x)=1/2×√(√(3)+√(2)×√(√(3)−√(2)решите алгебра 10-11 класс

Answer 1

$\displaystyle {\frac{\sqrt3}{2}}sinx-\frac{1}{2}cosx=\frac{1}{2}\sqrt{\sqrt3+\sqrt2}\cdot\sqrt{\sqrt3-\sqrt2}\\\\ sinxcos\frac{\pi}{6}-cosxsin\frac{\pi}{6}=\frac{1}{2}\sqrt{(\sqrt3)^2-(\sqrt2)^2}\\\\sin(x-\frac{\pi}{6})=\frac{1}{2}\\\\x-\frac{\pi}{6}=(-1)^n arcsin\frac{1}{2}+\pi n\\\\x=(-1)^n\frac{\pi}{6}+\frac{\pi}{6}+\pi n, \; n\in Z;$


$\displaystyle 1)\; x-\frac{\pi}{6}=\frac{\pi}{6}+2\pi n\\\\x=\frac{\pi}{3}+2\pi n, \; n\in Z;\\\\\\2)\; x-\frac{\pi}{6}=\pi-\frac{\pi}{6}+2\pi n\\\\ x=\pi-\frac{\pi}{6}+\frac{\pi}{6}+2\pi n \\\\ x=\pi +2\pi n, \; n\in Z.$