How do you solve cos2x= cosx from 0 to 2pi?

1 Answer
Apr 11, 2016

0, (2pi)/3, (4pi)/3, 2pi

Explanation:

Use the identity: cos 2x = 2cos^2 x - 1. The given equation
transforms to:
2cos^2 x - cos x - 1 = 0.
Solve this quadratic equation for cos x.
Since a + b + c = 0, use shortcut. There are 2real roots:
cos x = 1 and cos x = c/a = - 1/2.
a. cos x = 1 --> x = 0 or x = 2pi
b. cos x = - 1/2 ---> x = +- (2pi)/3
The co-terminal to arc - (2pi)/3 --> arc (4pi)/3

Answers for (0, 2pi):
0, (2pi)/3, (4pi)/3, 2pi