[m]1=sin^2 θ +cos^2 θ [/m]
то
[m]\frac{sin^2 θ -1}{cos^2 θ-1}=\frac{sin^2 θ -sin^2 θ -cos^2 θ}{cos^2 θ-sin^2 θ -cos^2 θ}=\frac{(-cos^2 θ)}{(-sin^2 θ) }=\frac{ cos^2 θ}{sin^2 θ }
Так как
[m]tg θ \cdot ctg θ =\frac{sin θ }{cos θ }\cdot \frac{cos θ }{sin θ }[/m]
то
[m]\frac{sin^2 θ -1}{cos^2 θ-1}+tg θ \cdot ctg θ =\frac{ cos^2 θ}{sin^2 θ }+1=\frac{ cos^2 θ+sin^2 θ }{sin^2 θ }=\frac{1}{cos^2 θ }[/m] - о т в е т