Question

Упростить
cos2a(1+tg^2a)-1

Answer 1

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