Precalculus (6th Edition) Blitzer

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

Chapter 8 - Section 8.2 - Inconsistent and Dependent Systems and Their Applications - Exercise Set - Page 905: 50


The solutions for the equation are $x=\frac{\pi }{2},\frac{3\pi }{2},\frac{\pi }{3},\frac{4\pi }{4},\frac{2\pi }{3},\frac{5\pi }{3}$.

Work Step by Step

$\begin{align} & \cos x\cdot {{\tan }^{2}}x=3\cos x \\ & \cos x\cdot {{\tan }^{2}}x-3\cos =0 \\ & \cos x\left( {{\tan }^{2}}x-3 \right)=0 \end{align}$ If $\cos x=0$ Then, $x=\frac{\pi }{2},\frac{3\pi }{2}$ $\begin{align} & {{\tan }^{2}}x-3=0 \\ & {{\tan }^{2}}x=3 \end{align}$ $\begin{align} & \tan x=\pm \sqrt{3} \\ & \tan x=\sqrt{3} \\ \end{align}$ $x=\frac{\pi }{3},\frac{4\pi }{4}$ $\tan x=-\sqrt{3}$ $\therefore x=\frac{2\pi }{3},\frac{5\pi }{3}$ Hence, the solutions for the equation are $x=\frac{\pi }{2},\frac{3\pi }{2},\frac{\pi }{3},\frac{4\pi }{4},\frac{2\pi }{3},\frac{5\pi }{3}$.
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