Question

Упростите:
$cos^{2} alpha -sin^{2} alpha -1/(sin alpha +cos alpha )^{2}-1$

Answer 1

(cos²α-sin²α-1)/(sinα+cosα)²-1)=( cos²α-sin²α- (cos²α+sin²α))/
( (sin²α+2sinαcosα+cos²α-1)=(  cos²α-sin²α- cos²α-sin²α)/
(1+sin2α-1)=-2sin²α/2sinα·cosα=-sinα/cosα=-tgα