Question

Упростить:

1) 1/cos^2 альфа- tg^2 альфа- sin^2 альфа

2) 1/cos^2 альфа- tg^2 альфа (cos^2альфа+1)

Answer 1

$1)~dfrac{1}{cos^2alpha}-tg^2alpha-sin^2alpha=tg^2alpha+1-tg^2alpha-sin^2alpha=1-sin^2alpha=cos^2alpha$

$2)~dfrac{1}{cos^2alpha}-tg^2alpha(cos^2alpha+1)=tg^2alpha+1-sin^2alpha-tg^2alpha=1-sin^2alpha=cos^2alpha$