Answer
$2-\sqrt3$.
Work Step by Step
We know that $\tan(A/2)=\frac{1-\cos A}{\sin A}$.
Hence here $\tan(\pi/12)=\frac{1-\cos \pi/6}{\sin \pi/6}=\frac{1-\frac{\sqrt3}{2}}{0.5}=2-\sqrt3$.
Trigonometry 7th Edition
by McKeague, Charles P.; Turner, Mark D.
Published by
Cengage Learning
ISBN 10:
1111826854
ISBN 13:
978-1-11182-685-7
Chapter 5 - Test - Page 315: 18
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