Find all solutions of the equation in the interval [0, 2π).
5 cos^3 x = 5 cos x
I'm not sure if I am approaching this problem properly.
5cos^3 (x) = 5 cos (x) ...... subtract 5 cos (x) from both sides
5cos^3(x) - 5 cos (x) = 0 .....divide through by 5
cos^3(x) - cos (x) = 0 ....factor
cos (x ) ( cos^2 (x) - 1) = 0
We have two equations to consider
cos (x ) = 0 and this happens at pi /2 and 3pi/2 in the given interval
Also
cos^2 ( x) - 1 = 0 ....add 1 to both sides
cos^2 (x ) = 1 take both roots
cos (x) = 1 or cos (x) = -1
This happens at This happens at
x = 0 x = pi
So...the solutions are
x = 0 , pi/2, pi, 3pi/2
Here's graph to confirm this : https://www.desmos.com/calculator/jx5rslbflo