Question

Доказать тождество: (1 - tg^2 A)/(1 + tg^2 A) = cos2A

Answer 1

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

Тождество доказано