Chapter 13.5, Problem 29CYU

To determine

To find : The value of $\theta$ .

Answer to Problem 29CYU

  $\theta =(2n+1)\frac{\pi }{3},n\in z,\frac{\pi }{3},\frac{5\pi }{3}$

Explanation of Solution

Given information :

We know that, the given information is $2{\cos }^2\theta =\cos \theta$

Calculation :

The given equation is

  $\begin{array}{l}2{\cos }^2\theta -\cos \theta =0\\ \Rightarrow \cos \theta [2\cos \theta -1]=0\\ \Rightarrow \cos \theta =0or2\cos \theta -1=0\\ \Rightarrow \theta =(2n+1)\frac{\pi }{2}or\cos \theta =\frac{1}{2}\\ \Rightarrow \theta =(2n+1)\frac{\pi }{2}or\theta =\frac{\pi }{3},\frac{5\pi }{3}\end{array}$