Question

How do you find all solutions of `2cos^2 3theta = cos 3theta`?

Answer 1

The answers are: `theta=pi/2+kpi` and `theta=pi/4+kpi/2`.

`2cos^3(3theta)-cos3theta=0rArrcostheta(2cos^2theta-1)=0rArr`

• `costheta=0rArrtheta=pi/2+kpi`, this means that `theta` can be `pi/2and3/2pi`.

• `2cos^2theta=1rArrcos^2theta=1/2rArrcostheta=+-sqrt(1/2)=+-1/sqrt2=+-sqrt2/2rArr` `theta=pi/4+kpi/2`,this means that `theta` can be `pi/4,3/4pi5/4pi,7/4pi`.