Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 6 - Section 6.6 - Vectors - Exercise Set - Page 785: 117


The value of $x$ is $\frac{\pi }{3},\frac{5\pi }{3},\pi $.

Work Step by Step

The trigonometric equation is $\begin{align} & {{\tan }^{2}}x-\sec x-1=0 \\ & \left( {{\sec }^{2}}x-1 \right)-\sec x-1=0 \\ & {{\sec }^{2}}x-\sec x-2=0 \\ & {{\sec }^{2}}x-2\sec x+\sec x-2=0 \end{align}$ And, $\begin{align} \left( \sec x-2 \right)\left( \sec x+1 \right)=0 & \\ \left( \sec x-2 \right)=0\text{ or }\left( \sec x+1 \right)=0 & \\ \sec x=2,-1 & \\ x=\frac{\pi }{3},\frac{5\pi }{3},\pi & \\ \end{align}$
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