Ctgb=-1/2 tg (a-b)=-1 ctga-?

[latex] tg (a-b)=-1 \\ \frac{tga-tgb}{1+tgatgb} =-1 \\ \frac{ \frac{1}{ctga} - \frac{1}{ctgb} }{1+ \frac{1}{ctgactgb} } =-1 \\ \frac{ \frac{1}{ctga} - \frac{1}{- \frac{1}{2} } }{1+ \frac{1}{ctga*(- \frac{1}{2})} } =-1 \\ \frac{ \frac{1}{ctga} +2 }{1- \frac{2}{ctga} } =-1 \\ \frac{1}{ctga} +2 =-1+ \frac{2}{ctga} \\ \frac{1}{ctga}=3 \\ ctga= \frac{1}{3}[/latex]