e)
cos^4\alpha-sin^4\alpha=cos^2\alpha-sin^2\alpha
cos^4\alpha-sin^4\alpha=(cos^2\alpha)^2-(sin^2\alpha)^2= (cos^2\alpha-sin^2\alpha)(cos^2\alpha+sin^2\alpha)=
=(cos^2\alpha-sin^2\alpha)(1-sin^2\alpha+sin^2\alpha)=cos^2\alpha-sin^2\alpha
g)
tg\alpha+ctg\alpha=\frac{1}{sin\alpha*cos\alpha}
tg\alpha+ctg\alpha=\frac{sin\alpha}{cos\alpha}+\frac{cos\alpha}{sin\alpha}=\frac{sin^2\alpha+cos^2\alpha}{sin\alpha*cos\alpha}=\frac{1}{sin\alpha*cos\alpha}