Question

Упростите выражение:
$(1- cos^{2} alpha )tg^{2} alpha +1-tg^{2} alpha$

Answer 1

$mathtt{(1-cos^2a)tg^2a+1-tg^2a=tg^2a(1-cos^2a-1)+1=}\mathtt{1-tg^2acos^2a=1-frac{sin^2a}{cos^2a}cos^2a=1-sin^2a=cos^2a}$