1)[latex] cos ^2x- 2cosx-3=0[/latex] 2)[latex]cos^4x-sin^4x= \sqrt{3/2} [/latex]

[latex]1)\;\cos^2x-2\cos x-3=0\\\cos x=t,\;\cos^2x=t^2,\;-1\leq t\;\leq1\\t^2-2t-3=0\\D=4+4\cdot3=16\\t_{1,2}=\frac{2\pm4}2\\t_1=-1\\t_2=3\;-\;He\;nogx.\\\cos x=-1\Rightarrow x=\pi+2\i n,\;n\in\mathbb{Z}\\\\2)\;\cos^4x-\sin^4x=\frac{\sqrt3}2\\(\cos^2x-\sin^2x)(\cos^2x+\sin^2x)=\frac{\sqrt3}2\\\cos2x=\frac{\sqrt3}2\\2x=\pm\frac\pi6+2\pi n\\x=\pm\frac\pi{12}+\pi n,\;n\in\mathbb{Z}[/latex]