Given that tan 𝑥 = 5

Question

12
𝑎𝑛𝑑 tan 𝑦 = 3
4
, find
tan(𝑥 + 𝑦)
A.
7
6
B.
16
33
C.
33
16
D.
56
33

Answer 1

We can use the tangent addition formula:

tan(𝑥 + 𝑦) = (tan 𝑥 + tan 𝑦) / (1 - tan 𝑥 tan 𝑦)

Substituting the given values, we get:

tan(𝑥 + 𝑦) = (5/12 + 3/4) / (1 - 5/12 * 3/4)

tan(𝑥 + 𝑦) = (5/12 + 9/12) / (1 - 15/48)

tan(𝑥 + 𝑦) = (14/12) / (33/48)

tan(𝑥 + 𝑦) = 56/33

Therefore, the answer is D. 56/33.