Question

$arctg \frac{1}{2} +arctg \frac{1}{3} = \pi /4$

Answer 1

Fie arctg(1/2) = x
tg(x) = 1/2
Fie arctg(1/3) = y
tg(y)=1/3
tg(x+y) = [tg(x)+tg(y)] / (1-tg(x) tg(y)
tg(x+y) = (1/2+1/3) / (1-1/6) = 1

Deoarece tg(π/4) = 1
x+y = π/4
In concluzie, arctg(1/2)+arctg(1/3)=π/4



Sa aratam si arctg(2)+arctg(3) = -π/4

Fie arctg(2) = x
tg(x)=2
Fie arctg(y) = 3
tg(y) = 3
tg(x+y) = [tg(x)+tg(y)] / (1-tg(x) tg(y)) = 5 / (1-6) =-5/-5=-1
tg(-π/4)= -1
In concluzie, x+y = -π/4

arctg(2)+arctg(3) = -π/4