Given that tan 𝑥 = 5

Question

Given that tan 𝑥 = 5

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.

Answer 2

To find tan(𝑥 + 𝑦), we can use the tangent addition formula which states that tan(𝑥 + 𝑦) = (tan 𝑥 + tan 𝑦) / (1 - tan 𝑥 * tan 𝑦).

Given that tan 𝑥 = 5/12 and tan 𝑦 = 3/4, we can substitute these values into the formula:

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

Now, let's simplify this expression:

tan(𝑥 + 𝑦) = (20/48 + 36/48) / (1 - 15/48)

tan(𝑥 + 𝑦) = 56/48 / (48/48 - 15/48)

tan(𝑥 + 𝑦) = 56/48 / 33/48

Next, let's simplify the expression by multiplying the numerator by the reciprocal of the denominator:

tan(𝑥 + 𝑦) = (56/48) * (48/33)

tan(𝑥 + 𝑦) = 56/33

Therefore, the answer is D. 56/33.