Question

Упростите выражения
(даю 80 баллов)

Answer 1

1)sin²x/cos²x +1=tg²x+1=1/cos²x
2)cosx/sinx-sinx/(1-cosx)=(cosx-cos²x-sin²x)/sinx(1-cosx)=(cosx-1)/sinx(1-cosx)=
=-1/sinx

Answer 2

$\frac{1- cos^2x}{1-sin^2x}+tgx*ctgx= \frac{sin^2x}{cos^2x}+1=tg^2x+1= \frac{1}{cos^2x}$

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