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

The equation to cos squared theta equals cos data has Solutions of-example-1
User Deepank
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1 Answer

11 votes
11 votes

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=(1)/(2) \end{gathered}

Hence


\begin{gathered} \cos \theta=0 \\ \text{and} \\ \cos \theta=(1)/(2) \end{gathered}

We can find the values of θ as follow

when cosθ = 0


\theta=(\pi)/(2),(3\pi)/(2)

When


\begin{gathered} \cos \theta=(1)/(2) \\ \theta=(\pi)/(3),(5\pi)/(3) \end{gathered}

Thus, the answer is:


\begin{gathered} \text{Option A} \\ (\pi)/(3),(\pi)/(2),(3\pi)/(2),(5\pi)/(3) \end{gathered}

User Astley
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