Maharashtra BoardEnglish MediumSTD 12 ScienceMathsTrigonometric Functions1 Mark
Question
Find the general solution of : $4 \cos ^2 \theta=1$
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Answer
We have $4 \cos ^2 \theta=1$
$\therefore \quad \cos ^2 \theta=\frac{1}{4}=\left(\frac{1}{2}\right)^2$
$\therefore \quad \cos ^2 \theta=\cos ^2 \frac{\pi}{3} $
The general solution of $\cos ^2 \theta=\cos ^2 \alpha$ is $\theta=n \pi \pm \alpha$, where $n \in Z$.
$\therefore \quad$ The general solution of $\cos ^2 \theta=\cos ^2 \frac{\pi}{3}$ is $\theta=n \pi \pm \frac{\pi}{3}$, where $n \in Z$.
$\therefore \quad$ The general solution of $4 \cos ^2 \theta=1$ is $\theta=n \pi \pm \frac{\pi}{3}$, where $n \in Z$.
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