How do you solve cos2x= cosxcos2x=cosx from 0 to 2pi?

1 Answer
Nghi N.
Apr 11, 2016

0, (2pi)/3, (4pi)/3, 2pi0,2π3,4π3,2π

Explanation:

Use the identity: cos 2x = 2cos^2 x - 1cos2x=2cos2x−1. The given equation
transforms to:
2cos^2 x - cos x - 1 = 02cos2x−cosx−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 = - 1/2cosx=ca=−12.
a. cos x = 1 --> x = 0 or x = 2pix=2π
b. cos x = - 1/2cosx=−12 ---> x = +- (2pi)/3x=±2π3
The co-terminal to arc - (2pi)/3−2π3 --> arc (4pi)/34π3

Answers for (0, 2pi)(0,2π):
0, (2pi)/3, (4pi)/3, 2pi0,2π3,4π3,2π

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