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

$1-tg^2a=\frac{-cos2a}{sin^2a}$

$1-\frac{sin^2a}{cos^2a}+\frac{cos2a}{sin^2a}=0$

$sin^2acos^2a-sin^4a+cos2acos^2a=0$

$(1-cos^2a)cos^2a-(1-cos^2a)^2+(2cos^2a-1)cos^2a=0$

$cos^2a-cos^4a-1+2cos^2a-cos^4a+2cos^4a-cos^2a=0$

$2cos^2a-1=0$

$cos^2a=\frac12$

$cosa=\frac{1}{\sqrt2}$

$a=\frac{\pi}{4}+2\pi n$ ,n∈Z

$cosa=-\frac{1}{\sqrt2}$

$a=\frac{3\pi}{4}+2\pi n$ ,n∈Z