Question

tg(a+ pi/4)=-1/3 то значение ctg2a=

Answer 1

tg(a-π/4)=(tga-tgπ/4)/(1+tga×tgπ/4)=(tga-1)/(1+tga)
(tga-1)/(1+tga)=-1/3
3×(tga-1)=-1×(1+tga)
3tga-3=-1-tga
4tga=2
tga=1/2
tg2a=2tga/(1-tg²a)=(2×1/2)/(1-(1/2)²)=1/(3/4)=4/3
ctg2a=1/tg2a=3/4