Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 7 - Section 7.3 - Double-Angle, Half-Angle, and Product-Sum Formulas - 7.3 Exercises: 26

Answer

$2+\sqrt{3}$

Work Step by Step

Use the half-angle formula, $\tan\frac{u}{2}=\frac{1-\cos u}{\sin u}$. $\tan \frac{5\pi}{12}$ $=\tan \frac{ \frac{5\pi}{6}}{2}$ $=\frac{1-\cos \frac{5\pi}{6}}{\sin \frac{5\pi}{6}}$ $=\frac{1-(-\frac{\sqrt{3}}{2})}{\frac{1}{2}}$ $=\frac{(1+\frac{\sqrt{3}}{2})*2}{\frac{1}{2}*2}$ $=\frac{2+\sqrt{3}}{1}$ $=2+\sqrt{3}$
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