Упростите:
[tex] cos^{2} \alpha -sin^{2} \alpha -1/(sin \alpha +cos \alpha )^{2}-1[/tex]

(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