Question

Упростить выражение. памагитииии

Answer 1

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