1\\\\a)\ \ sinx=-\dfrac{\sqrt3}{2}\ \ ,\ \ x=(-1)^{n+1}\cdot \dfrac{\pi}{3}+\pi n\, \ n\in Z" alt="2cos^2x-3\sqrt3\, cos\Big(\dfrac{3\pi}{2}-x\Big)+4=0\\\\2cos^2x-3\sqrt3\cdot (-sinx)+4=0\\\\2(1-sin^2x)+3\sqrt3\cdot sinx+4=0\\\\2-2sin^2x+3\sqrt3\cdot sinx+4=0\\\\2sin^2x-3\sqrt3\, sinx-6=0\ \ ,\ \ \ \ \ -1\leq sinx\leq 1\ ,\\\\D=27+48=75\ \ ,\ \ \ \ \sqrt{75}=\sqrt{25\cdot 3}=5\sqrt3\\\\sinx=\dfrac{3\sqrt3-5\sqrt3}{4}=-\dfrac{\sqrt3}{2}\ \ ili\ \ \ sinx=\dfrac{3\sqrt3+5\sqrt3}{4}=2\sqrt3>1\\\\a)\ \ sinx=-\dfrac{\sqrt3}{2}\ \ ,\ \ x=(-1)^{n+1}\cdot \dfrac{\pi}{3}+\pi n\, \ n\in Z" align="absmiddle" class="latex-formula">
1\ .\\\\Otvet:\ \ x=(-1)^{n+1}\cdot \dfrac{\pi}{3}+\pi n\ ,\ n\in Z\ ." alt="b)\ \ sinx=2\sqrt3\ \ \Rightarrow \ \ x\in \varnothing \ ,\ \ t.k.\ \ -1\leq sinx\leq 1\ \ i\ \ 2\sqrt3>1\ .\\\\Otvet:\ \ x=(-1)^{n+1}\cdot \dfrac{\pi}{3}+\pi n\ ,\ n\in Z\ ." align="absmiddle" class="latex-formula">