Question

Demonstrati ca, daca

ctg x = 2

ctg y = 3

si

x,y ∈ (0, π/2)

atunci

x + y = π/4

Answer 1

Răspuns:

Explicație pas cu pas:

tgx=1/2

tgy=1/3

tg(x+y) = (1/2+1/3)/(1-1/6)= (5/6)/(5/6) =1

x+y= kπ+arctg1= kπ+π/4, k∈Z

dar x,y ∈ (0, π/2) deci   x+y∈(0.π), convine k=0

x + y = π/4,  C.C.T.D.