Question

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

Answer 1

$frac{1-tg^{2}alpha}{1+tg^{2}alpha}=frac{1-frac{Sin^{2} alpha }{Cos^{2}alpha}}{1+frac{Sin^{2}alpha}{Cos^{2}alpha}}=frac{(Cos^{2}alpha-Sin^{2}alpha)*Cos^{2}alpha}{(Cos^{2}alpha+Sin^{2}alpha)*Cos^{2}alpha}=frac{Cos2alpha }{1}=Cos2alpha\\Cos2alpha=Cos2alpha$

Тождество доказано