Răspuns:
Explicație pas cu pas:
tg (α + β) / tg β = [sin (α + β) · cos β] / [cos (α + β) · sin β] =
sin (α + β) · cos β = [sin (α + 2β) + sin α] / 2 = (3 sin α + sin α) / 2 =
= (4sin α) / 2 = 2sinα
cos (α + β) · sin β = [sin (α + 2β) - sin α] / 2 = (3 sin α - sin α) / 2 =
= (2sin α) / 2 = sinα
⇒ tg (α + β) / tg β = 2sinα / sinα = 2
