Упростите выражеия: числитель соs²a-1 знаменатель1-sin²a - tg a ctg...

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

sin²a+cos²a+ctg²a=1+ctg²a= $\frac{1}{sin^2\alpha}$

$tgx-\frac{cosx}{1-sinx}=\frac{sinx}{cosx}-\frac{cosx}{1-sinx}=\frac{sinx-sin^2x-cos^2x}{cosx(1-sinx)}=$

$=\frac{sinx-(sin^2x+cos^2x)}{cosx(1-sinx)}=\frac{sinx-1}{cosx(1-sinx)}=-\frac{1}{cosx}$

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

.......................................................................................................