Question

Выразить через соs: sin^4-cos^4​

Answer 1

$\displaystyle\bf\\Sin^{4}\alpha -Cos^{4} \alpha = (Sin^{2}\alpha)^{2} -(Cos^{2} \alpha)^{2} =\\\\\\=\underbrace{(Sin^{2} \alpha +Cos^{2} \alpha )}_{1}\cdot(Sin^{2} \alpha -Cos^{2} \alpha )=\\\\\\=Sin^{2} \alpha -Cos^{2} \alpha =-(\underbrace{Cos^{2} \alpha -Sin^{2} \alpha )}_{Cos2\alpha }=-Cos2\alpha$