Question

Упростите выражение

Answer 1

$\frac{Cos^{4}-Sin^{4}\alpha}{(1-Sin\alpha)(1+Sin\alpha)}+2tg^{2}\alpha-\frac{1}{Cos^{2}\alpha}=\frac{(Cos^{2}\alpha+Sin^{2}\alpha)(Cos^{2}\alpha-Sin^{2}\alpha)}{1-Sin^{2} \alpha }+2tg^{2}\alpha-(tg^{2}\alpha+1)=\frac{Cos^{2}\alpha-Sin^{2}\alpha}{Cos^{2}\alpha}+2tg^{2}\alpha-tg^{2}\alpha-1=1-tg^{2}\alpha+tg^{2} \alpha-1=0$