Question

Textbook: Please write as an expression involving functions of Θ alone.

Question: tan(Θ + 30°)

Answer: √3 tanΘ +1 / √3 - tanΘ

I need work showing how to get the answer. Thank You!

Answer 1

Explanation:

tan(Θ + 30°)

Use angle sum formula:

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

So we can write this as:

(tan Θ + tan 30°) / (1 − tan Θ tan 30°)

tan 30° = 1/√3, so:

(tan Θ + 1/√3) / (1 − 1/√3 tan Θ)

Multiply top and bottom by √3:

(√3 tan Θ + 1) / (√3 − tan Θ)