AFA 1988 Trigonometria
Se `\text{tg}(x + y) = 33` e `\text{tg}x =3`, então `\text{tg}y` é igual a:
(A) `-10/3`
(B) `-3/10`
(C) `3/10`
(D) `2/3`
Da relação `\text{tg}(x+y)=\frac{\text{tg}x + \text{tg}y}{1-\text{tg}x \cdot \text{tg}y}` vem que:
`\text{tg}(x+y)=\frac{\text{tg}x + \text{tg}y}{1-\text{tg}x \cdot \text{tg}y}`
`33=\frac{3 + \text{tg}y}{1-3\text{tg}y}`
`33(1-3\text{tg}y)=3 + \text{tg}y`
`33-99\text{tg}y=3 + \text{tg}y`
`-99\text{tg}y-\text{tg}y=3 -33`
`-100\text{tg}y=-30`
`100\text{tg}y=30/100 =3/10`