Докажите : 1) cos^4a-sin^4a+sin^2a=cos^2a 2) (sin^2+tg^2a+cos^2a)*(cos^2+tga*ctga)=2

Решите задачу:

$1) cos^{4} a-sin^{4} \alpha +sin ^{2} \alpha =cos^{2} \alpha \\ cos^{4} \alpha -sin ^{4} \alpha +sin ^{2} \alpha =(cos ^{4} \alpha -sin ^{4} \alpha )+sin ^{2} \alpha =$ $=(cos^{2} \alpha -sin ^{2} \alpha )+sin ^{2} \alpha =1(cos ^{2} \alpha -sin^{2} \alpha )+sin ^{2} \alpha =cos ^{2} \alpha \\ cos^{2} a=cos^{2} a$
$[tex](sin ^{2} \alpha +tg ^{2} \alpha +cos ^{2} \alpha )(cos ^{2} \alpha +tg \alpha ctg \alpha )=2 \\ (1+tg ^{2} \alpha )*(cos ^{2} \alpha +1)=cos ^{2} \alpha +1+cos ^{2} \alpha tg ^{2} \alpha +tg ^{2} \alpha = \\ cos ^{2} a+1+cos ^{2} \alpha * \frac{sin ^{2} \alpha }{cos ^{2} \alpha } +tg ^{2} \alpha =cos ^{2} \alpha +1+sin ^{2} \alpha +tg ^{2} a= \\ =2+tg ^{2} \alpha$