-\frac{\pi}{6}\\\\2sin^2x-5sinx-3=0\; ,\; \; D=49\; ,\; \; sinx=-\frac{1}{2}\; \; ili\; \; sinx=3\\\\1)\; \; sinx=3\; \; \Rightarrow \; \; x\in \varnothing\; ,\; t.k.\; |sinx|\leq 1\\\\2)\; \; sinx=-\frac{1}{2}\; \; \to \; \; \left [ {{x=-\frac{\pi}{6}+2\pi n\; ,\; n\in Z} \atop {x=-\frac{5\pi}{6}+2\pi n,\; n\in Z}}} \right." alt="\frac{2sin^2x-5sinx-3}{\sqrt{x+\frac{\pi}{6}}}=0\; \; ,\; \; ODZ:\; \left \{ {{x+\frac{\pi }{6}\geq 0} \atop {x+\frac{\pi}{6}\ne0}} \right. \; \; \to \; \; x>-\frac{\pi}{6}\\\\2sin^2x-5sinx-3=0\; ,\; \; D=49\; ,\; \; sinx=-\frac{1}{2}\; \; ili\; \; sinx=3\\\\1)\; \; sinx=3\; \; \Rightarrow \; \; x\in \varnothing\; ,\; t.k.\; |sinx|\leq 1\\\\2)\; \; sinx=-\frac{1}{2}\; \; \to \; \; \left [ {{x=-\frac{\pi}{6}+2\pi n\; ,\; n\in Z} \atop {x=-\frac{5\pi}{6}+2\pi n,\; n\in Z}}} \right." align="absmiddle" class="latex-formula">
-\frac{\pi }{6}\; ,\; \; 2\pi n>0\; ,\; \; n>0\\\\n=1:\; x=-\frac{\pi }{6}+2\pi =\frac{11\pi }{6}\; ,\\\\n=2:\; \; x=-\frac{\pi}{6}+4\pi =\frac{23\pi }{6}\; ,\, ...\\\\b)\; \; -\frac{5\pi }{6}+2\pi n>-\frac{\pi}{6}\; ,\; \; 2\pi n>\frac{4\pi }{6}\; ,\; \; 2\pi n>\frac{2\pi }{3}\; ,\; \; n>\frac{1}{3}\\\\n=1:\; \; x=-\frac{5\pi}{6}+2\pi =\frac{7\pi }{6}\; ,\\\\n=2:\; \; x=-\frac{5\pi }{6}+4\pi =\frac{19\pi }{6}\; ,\, ...\\\\Otvet:\; \; x_1=\frac{7\pi }{6}+2\pi n\; \; \; ili\; \; \; x_2=\frac{11\pi }{6}+2\pi n\; ,\; \; n\in Z\; ." alt="3)\; a)\; -\frac{\pi }{6}+2\pi n>-\frac{\pi }{6}\; ,\; \; 2\pi n>0\; ,\; \; n>0\\\\n=1:\; x=-\frac{\pi }{6}+2\pi =\frac{11\pi }{6}\; ,\\\\n=2:\; \; x=-\frac{\pi}{6}+4\pi =\frac{23\pi }{6}\; ,\, ...\\\\b)\; \; -\frac{5\pi }{6}+2\pi n>-\frac{\pi}{6}\; ,\; \; 2\pi n>\frac{4\pi }{6}\; ,\; \; 2\pi n>\frac{2\pi }{3}\; ,\; \; n>\frac{1}{3}\\\\n=1:\; \; x=-\frac{5\pi}{6}+2\pi =\frac{7\pi }{6}\; ,\\\\n=2:\; \; x=-\frac{5\pi }{6}+4\pi =\frac{19\pi }{6}\; ,\, ...\\\\Otvet:\; \; x_1=\frac{7\pi }{6}+2\pi n\; \; \; ili\; \; \; x_2=\frac{11\pi }{6}+2\pi n\; ,\; \; n\in Z\; ." align="absmiddle" class="latex-formula">