Question

ctg(45-a) - ctg(45+a)

Answer 1

$star ; ; ctgx-ctgy=frac{cosx}{sinx}-frac{cosy}{siny}=frac{cosx, siny-sinx, cosy}{sinxcdot siny}=frac{sin(y-x)}{sinxcdot siny}; star \\\ctg(45-a)-ctg(45+a)=frac{sin(45+a-(45-a))}{sin(45-a)cdot sin(45+a)}=frac{sin2a}{frac{1}{2}(cos2a-cos90)} =\\= frac{2, sin2a}{cos2a} =2cdot tg2a\\\star ; ; sinxcdot siny=frac{1}{2}cdot (cos(x-y)-cos(x+y)); ; star$