Question

Find the exact value using a sum or difference formula: tan(31π/12)

A) -1
B) 0
C) 1
D) Undefined

Answer 1

The exact value of tan(31π/12) using a sum or difference formula is undefined.

Step-by-step explanation:

To find the exact value of tan(31π/12) using a sum or difference formula, we can first convert 31π/12 into degrees. There are 360 degrees in a circle, so 31π/12 is approximately 262.5°. Now, we can use the sum formula for tangent:

tan(A+B) = (tan(A) + tan(B))/(1 - tan(A)tan(B))

Since we're finding the tangent of a single angle, we can rewrite the formula as:

tan(31π/12) = (tan(270°) + tan(262.5°))/(1 - tan(270°)tan(262.5°))

By evaluating the tangent values and plugging them into the formula, we find that the exact value of tan(31π/12) is undefined (option D).