1\;-\;He\;nogx.\\\sin x=-\frac12\Rightarrow x=(-1)^n\cdot\frac{7\pi}6+\pi n,\;n\in\mathbb{Z}" alt="\sin x+\cos^2x=\frac14\\\sin x+1-\sin^2x=\frac14\\\sin^2x-\sin x-\frac34=0\;\;\times 4\\4\sin^2x-4\sin x-3=0\\\sin x=t,\;\sin^2x=t^2,\;t\in[-1;\;1]\\4t^2-4t-3=0\\D=16+4\cdot4\cdot3=64\\t_{1,2}=\frac{4\pm8}{8}\\t_1=-\frac12\\t_2=\frac32>1\;-\;He\;nogx.\\\sin x=-\frac12\Rightarrow x=(-1)^n\cdot\frac{7\pi}6+\pi n,\;n\in\mathbb{Z}" align="absmiddle" class="latex-formula">