Theory question 104
TrigonometryGiven that tan 2A = 2 tan A/(1 − tan2A), evaluate tan 15° leaving your answer in surd form.
Show the model answer
Model answer
Put A = 15°: tan 30° = 1/√3 = 2t/(1 − t2), t = tan 15°
t2 + 2√3t − 1 = 0
t = −√3 ± 2
tan 15° > 0, so tan 15° = 2 − √3
Explanation
Use the double-angle formula with 2A = 30° and keep the positive root.