Question

se tgA=1/7 e senB=1/√10, com 0<B<π/2, calcule tg(A+B)

Answer 1

Vamos la

se tg(A) =1/7 e sen(B) = 1/√10, com 0<B<π/2, calcule tg(A+B)

sen²(B) + cos²(B) = 1

1/10 + cos²(b) = 10/10

cos²(b) = 9/10 ,  cos(b) = 3/√10

tg(B) = sen(B)/cos(B) = 1/3

agora

tg(A + B) = (tg(A) + tg(B))/(1 - tg(A)*tg(B))

tg(A + B) = (1/7 + 1/3)/(1 - (1/7)*(1/3)) = (10/21)/(1 - 1/21)

tg(A + B) = (10/21)/(20/21) = 10/20 = 1/2