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

[latex]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 = [/latex][latex]=(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[/latex] [latex][latex](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 [/latex]

1) cos⁴a-sin⁴a+sin²a=cos²a  (cos²a-sin²a)(cos²a+sin²a)+sin²a=cos²a (cos²a-sin²a) *1+sin²a=cos²a cos²a-sin²a+sin²a=cos²a cos²a=cos²a 2) (sin²a+tg²a+cos²a)*(cos²a+tga*ctga)=2 (1+tg²a)(cos²a+1)=2    [latex](1+tg^{2}a)(cos^{2}a+1)= \frac{1}{cos^{2}a}* (cos^{2}a+1)= \frac{cos^{2}a}{cos^{2}a} +\frac{1}{cos^{2}a}= \\ 1+\frac{1}{cos^{2}a}=1+1+ tg^{2}a=2+tg^{2}a \\ [/latex]