Solve the equation tan2 x cos x = tan2 x on the interval [0, 2π).

Answered: Solve the equation tan2 x cos x = tan2…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 57E

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Question

Solve the equation tan² x cos x = tan² x on the interval [0, 2π).

Expert Solution

Step 1

We have given the equation as

$\tan^{2} (x) = \cos (x) \tan^{2} (x)$

Rearranging the term in left hand side and on solving further, we get the result as

$\begin{array}{rcl} \tan^{2} (x) - \cos (x) \tan^{2} (x) & = & 0 \\ \tan^{2} (x) [1 - \cos (x)] & = & 0 \\ \tan x & = & 0 a n d 1 - \cos x = 0 \\ \tan x & = & 0 a n d \cos x = 1 \end{array}$

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