Question

ctga - 1/1-tga + ctga-1 срочно надо

Answer 1

$frac{overbrace {ctgx-1}}{1-tgx}+underbrace {ctgx-1}=(ctgx-1)cdot ( frac{1}{1-tgx} +1)= \\=(frac{cosx}{sinx}-1)cdot (frac{1}{1-frac{sinx}{cosx}}+1)= frac{cosx-sinx}{sinx}cdot ( frac{cosx}{cosx-sinx}+1)=\\= frac{cosx}{sinx} + frac{cosx-sinx}{sinx} = frac{2cosx-sinx}{sinx} = frac{2cosx}{sinx} -frac{sinx}{sinx} =2ctgx-1\\ili$

$frac{ctgx-1}{1-tgx} +ctgx-1=frac{frac{cosx}{sinx}-1}{1-frac{sinx}{cosx}} +ctgx-1=frac{(cosx-sinx)cosx}{(cosx-sinx)sinx}+ctgx-1=\\= frac{cosx}{sinx}+ctgx-1=ctgx+ctgx-1=2ctgx-1$