Question

Выражеия: числитель соs²a-1 знаменатель1-sin²a - tg a ctg a sin²a+cos²a+ctg²a tg x- cos x /1-sin x cos²(-a)/1+sin(a) умоляю !

Answer 1

$sin^2a+cos^2a+ctg^2a = 1+ctg^2a=\frac{1}{sin^2a}$

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

$\frac{cos^2a-1}{1-sin^2a }-tga*ctga = \frac{-sin^2a}{cos^2a}-1 = -tg^2a-1$

Answer 2

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

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

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

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

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

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