Question

Wyznacz tg2y wiedzac ze tgx=2 i tg(x+y)=1.

Answer 1

Tg(x+y)=1
(tgx+tgy)/(1-tgx*tgy)=1
(2+tgy)/(1-2tgy)=1
2+tgy=1-2tgy
3tgy=-1
tgy=-1/3
tg2y=(2tgy)/(1-tg²y)
tg2y=(-2/3)/(1-1/9)
tg2y=(-2/3)*(9/8)
tg2y=-3/4