Question

Упрости выражение:
$\frac{cos(2\alpha )}{cos^{2}\alpha }$

Answer 1

$\displaystyle\bf\\\frac{Cos2\alpha }{Cos^{2}\alpha } =\frac{2Cos^{2}\alpha -1 }{Cos^{2} \alpha } =\frac{2Cos^{2}\alpha }{Cos^{2} \alpha } -\frac{1}{Cos^{2} \alpha } =2-(1+tg^{2} \alpha )=\\\\=2-1-tg^{2} \alpha=1-tg^{2} \alpha$