Question

Решите, пожалуйста, очень срочно нужно

Answer 1

$\frac{Cos^{4}\alpha-Sin^{4}\alpha}{Cos^{2}\alpha}+2tg^{2}\alpha=\frac{(Cos^{2}\alpha-Sin^{2}\alpha)(Cos^{2}\alpha +Sin^{2} \alpha)}{Cos^{2}\alpha}+\frac{2Sin^{2}\alpha}{Cos^{2}\alpha}=\frac{Cos^{2}\alpha-Sin^{2}\alpha+2Sin^{2}\alpha}{Cos^{2}\alpha} =\frac{Cos^{2}\alpha+Sin^{2}\alpha}{Cos^{2}\alpha}=\frac{1}{Cos^{2}\alpha} \\\\\frac{1}{Cos^{2} \alpha }=\frac{1}{Cos^{2}\alpha}$

Тождество доказано