Question

Tg(pi/4+a)= -1/3, найти cotg 2a

Answer 1

Tg(α+β) = (tg(α) + tg(β))/(1 - tg(α)·tg(β))tg(π/4+a) = (1 + tga)/(1 - tgα)
(1 + tga)/(1 - tgα)=-1/3   1+tga=-1/3/(1 - tgα)=-1/3+1/3tga
2/3tga=-4/3   tga=-4/3*3/2=-2   ctga=-1/2

ctg2a  =  (ctga - tga)/2
ctg2a=(-1/2+2)/2=3/4