Question

Упростите 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 помочь!

 

 

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

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

 

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

 

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

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

 

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

 

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