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

1 Answer
Massimiliano
Feb 6, 2015

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=+-sqrt2/2rArrtheta=pi/4+kpi/2,this means that theta can be pi/4,3/4pi5/4pi,7/4pi.

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