Precalculus (6th Edition) Blitzer

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

Chapter 5 - Section 5.5 - Trigonometric Equations - Exercise Set - Page 704: 52


No solution.

Work Step by Step

We have to solve the equation on the interval $[0,2\pi )$; follow the course of action given below: $\begin{align} & 4{{\sec }^{2}}x-2=0 \\ & 4{{\sec }^{2}}x=0+2 \\ & {{\sec }^{2}}x=\frac{2}{4} \\ & {{\sec }^{2}}x=\frac{1}{2} \end{align}$ And the above expression can be further simplified as: $\begin{align} & \frac{1}{{{\cos }^{2}}x}=\frac{1}{2} \\ & \text{co}{{\text{s}}^{2}}x=2 \\ & \cos x=\pm \sqrt{2} \end{align}$ The value of $\cos x$ cannot exceed 1. In this expression $\cos x=\pm \sqrt{2}$. Hence, it will not be a part of the solution.
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