Find all solutions of the equation in the interval [0, 2?). (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.) 5 cos3 x = 5 cos x

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.2: Trigonometric Equations
Problem 61E
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Find all solutions of the equation in the interval [0, 2?). (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)

5 cos3 x = 5 cos x 
Expert Solution
Step 1

Solution ) 5cos3x = 5cosx

5cos3x - 5cosx = 0

5cosx ( cos2x - 1 ) = 0

cosx ( cos2x - 1 ) = 0

From this cos x = 0 , 

[cos ( 2n + 1)π/2  = 0]

 cos2x - 1 = 0

cos2x = 1

cos x ,= 1

[ cos 2nπ = 1 ]

x = 0 , π/2 , π, 3π/2

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