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 - Page 561: 23



Work Step by Step

Use the half-angle formula, $\tan\frac{u}{2}=\frac{1-\cos u}{\sin u}$. $\tan \frac{\pi}{8}$ $=\tan \frac{ \frac{\pi}{4}}{2}$ $=\frac{1-\cos \frac{\pi}{4}}{\sin \frac{\pi}{4}}$ $=\frac{1-\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}}$ $=\frac{(1-\frac{\sqrt{2}}{2})*\sqrt{2}}{\frac{\sqrt{2}}{2}*\sqrt{2}}$ $=\frac{\sqrt{2}-\frac{2}{2}}{\frac{2}{2}}$ $=\frac{\sqrt{2}-1}{1}$ $=\sqrt{2}-1$
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