Answer
$2+\sqrt3$.
Work Step by Step
We know that $\cot(A/2)=\frac{\sin A}{1-\cos A}$.
Hence here $\cot \pi/12=\frac{\sin\pi/6}{1-\cos\pi/6}=\frac{0.5}{1-\frac{\sqrt3}{2}}=2+\sqrt3$.
Trigonometry 7th Edition
by McKeague, Charles P.; Turner, Mark D.
Published by
Cengage Learning
ISBN 10:
1111826854
ISBN 13:
978-1-11182-685-7
Chapters 1-8 - Cumulative Test - Page 477: 14
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