Question

the equation to cos squared theta equals cos data has Solutions of

Answer 1

Given the domain

$0\le\theta<2\pi$

The equation

$2\cos ^2\theta=\cos \theta$

To simplify,

$\begin{gathered} \text{let} \\ x=\cos \theta \end{gathered}$

so that

$2x^2=x$

Then we will have

$2x^2-x=0$

We will have

$\begin{gathered} x(2x-1)=0 \\ \text{Thus} \\ x=0 \\ \text{and} \\ x=\frac{1}{2} \end{gathered}$

Hence

$\begin{gathered} \cos \theta=0 \\ \text{and} \\ \cos \theta=\frac{1}{2} \end{gathered}$

We can find the values of θ as follow

when cosθ = 0

$\theta=\frac{\pi}{2},\frac{3\pi}{2}$

When

$\begin{gathered} \cos \theta=\frac{1}{2} \\ \theta=\frac{\pi}{3},\frac{5\pi}{3} \end{gathered}$

Thus, the answer is:

$\begin{gathered} \text{Option A} \\ \frac{\pi}{3},\frac{\pi}{2},\frac{3\pi}{2},\frac{5\pi}{3} \end{gathered}$