Tg(a+pi/4)=-1/3 то значение ctg2a

Question

Tg(a+pi/4)=-1/3 то значение ctg2a

Answer 1

1) tg(α+π/4) = (tgα + tgπ/4) / (1 - tgα*tgπ/4) = (tgα + 1)/(1 - tgα) = -1/3
3(tgα + 1) = tgα -1
3tgα  + 3 = tgα - 1
2tgα = -4
tgα = -2
2) Ctg2α = (1 - tg²α)/2tgα = (1 - 4)/(-4) = 3/4 = 0,75