1" alt="cos2x+2=\sqrt3cos(\frac{3\pi}{2}-x)\\\\\star \; cos2x=cos^2x-sin^2x=(1-sin^2x)-sin^2x=1-2sin^2x\; \star \\\\1-2sin^2x+2=\sqrt3\cdot (-sinx)\\\\2sin^2x-\sqrt3\cdot sinx-3=0\\\\D=3+4\cdot 2\cdot 3=27\\\\a)\; \; (sinx)_1= \frac{\sqrt3-\sqrt{27}}{4} = \frac{\sqrt3-3\sqrt3}{4} =-\frac{\sqrt3}{2}\\\\x=(-1)^{k}arcsin(-\frac{\sqrt3}{2})+\pi k=(-1)^{k+1}\cdot \frac{\pi}{3}+\pi k\; ,\; k\in Z\\\\b)\; \; (sinx)_2=\frac{\sqrt3+3\sqrt3}{4}=\sqrt3>1" align="absmiddle" class="latex-formula">
нет решений, так как -1≤sinx≤1 .
![x\in [-3\pi ,-\frac{3\pi}{2}\, ]\; :\; \; x=-\frac{7\pi}{3}\; ;\; -\frac{8\pi}{3}\; .](https://tex.z-dn.net/?f=x%5Cin+%5B-3%5Cpi+%2C-%5Cfrac%7B3%5Cpi%7D%7B2%7D%5C%2C+%5D%5C%3B+%3A%5C%3B+%5C%3B+x%3D-%5Cfrac%7B7%5Cpi%7D%7B3%7D%5C%3B+%3B%5C%3B+-%5Cfrac%7B8%5Cpi%7D%7B3%7D%5C%3B+. "x\in [-3\pi ,-\frac{3\pi}{2}\, ]\; :\; \; x=-\frac{7\pi}{3}\; ;\; -\frac{8\pi}{3}\; .")