Question

упростить выражение1+ctg(2альфа-3/2пи)ctg(3/2пи+альфа)

Answer 1

1+ctg(2alfa-1.5pi)*ctg(1.5pi+alfa)

ctg(2alfa-1.5pi+1.5pi+alfa)+1

ctg(3alfa)+1

Answer 2

$1+ctg(2alpha-frac{3}{2}pi)cdot ctg(frac{3}{2}pi+alpha)=1-ctg(frac{3}{2}pi-2alpha)cdot ctg(frac{3}{2}pi+alpha)=$

 

$=1-tg2alphacdot(-tgalpha)=1+tg2alphacdot tgalpha=1+frac{sin2alpha}{cos2alpha}cdot frac{sinalpha}{cosalpha}=$

 

$=1+frac{2cdot sinalphacdot cosalphacdot sinalpha}{cos2alphacdot cosalpha}=1+frac{2cdot sin^2alpha}{cos2alpha}=1+frac{1-cos2alpha}{cos2alpha}=frac{cos2alpha+1-cos2alpha}{cos2alpha}=$

 

$=frac{1}{cos2alpha}$