Question

Cos'2a(1-tg'2a) спростити вираз

Answer 1

$Cos^{2}\alpha(1-tg^{2} \alpha)=Cos^{2}\alpha*(1-\frac{Sin^{2}\alpha}{Cos^{2}\alpha})=Cos^{2}\alpha*\frac{Cos^{2}\alpha-Sin^{2}\alpha}{Cos^{2}\alpha} =\\\\=Cos^{2}\alpha-Sin^{2}\alpha=\boxed{Cos2\alpha}$