Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

Chapter 6 - Section 6.3 - Trigonometric Equations Involving Multiple Angles - 6.3 Problem Set - Page 340: 34


$$x= \frac{3\pi}{10}+ \frac{2k\pi}{5}$$

Work Step by Step

Given $$ \sin 3x \cos 2x + \cos3x \sin2 x=-1 $$ Then by using $\sin(A+B)= \sin A \cos B+ \cos A \sin B$ , we get \begin{align*} \sin 3x \cos 2x + \cos3x \sin2 x&=-1\\ \sin(5x)&=-1\\ \end{align*} We find all possible solutions for $x$ $$ 5x=\frac{3\pi}{2}+2k\pi \ \Rightarrow x= \frac{3\pi}{10}+ \frac{2k\pi}{5}$$
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