1-tg^2a=(-cos2a)/sin^2a

[latex]1-tg^2a=\frac{-cos2a}{sin^2a}[/latex] [latex]1-\frac{sin^2a}{cos^2a}+\frac{cos2a}{sin^2a}=0[/latex] [latex]sin^2acos^2a-sin^4a+cos2acos^2a=0[/latex] [latex](1-cos^2a)cos^2a-(1-cos^2a)^2+(2cos^2a-1)cos^2a=0[/latex] [latex]cos^2a-cos^4a-1+2cos^2a-cos^4a+2cos^4a-cos^2a=0[/latex] [latex]2cos^2a-1=0[/latex] [latex]cos^2a=\frac12[/latex] [latex]cosa=\frac{1}{\sqrt2}[/latex]  [latex]a=\frac{\pi}{4}+2\pi n[/latex],n∈Z [latex]cosa=-\frac{1}{\sqrt2}[/latex] [latex]a=\frac{3\pi}{4}+2\pi n[/latex],n∈Z