Question

Упростить
cos2a(1+tg^2a)-1

Answer 1

$\displaystyle \tt cos\:(\alpha)^2\cdot(1+tg\:(\alpha)^2)-1=cos\:(\alpha)^2\cdot\bigg(1+\bigg(\frac{sin\:(\alpha)}{cos\:(\alpha)}\bigg)^2\:\bigg)-1=\\\\\\ \displaystyle \tt =cos\:(\alpha)^2\cdot\bigg(1+\frac{sin\:(\alpha)^2}{cos\:(\alpha)^2}\bigg)-1=cos\:(\alpha)^2\cdot\frac{cos\:(\alpha)^2+sin\:(\alpha)^2}{cos\:(\alpha)^2}-1=\\\\\\ \displaystyle \tt =1-1=\underline{\bold{0}}$