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

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

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