Find the general solution of : 4 = 3 2 - Vidyadip

Question

Find the general solution of : $\sin 4 \theta=\frac{\sqrt{3}}{2}$

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Answer

$\text { } \sin 4 \theta=\frac{\sqrt{3}}{2}$
$\therefore \quad \sin 4 \theta=\sin \frac{\pi}{3} $
The general solution of $\sin \theta=\sin \alpha$ is $\theta=n \pi+(-1)^{ n } \alpha$, where $n \in Z$.
$\therefore \quad$ The general solution of $\sin 4 \theta=\sin \frac{\pi}{3}$ is $4 \theta=n \pi+(-1)^{ n } \frac{\pi}{3}$, where $n \in Z$.
$\therefore \quad$ The general solution of $\sin 4 \theta=\frac{\sqrt{3}}{2}$ is $\theta=\frac{n \pi}{4}+(-1)^{ n } \frac{\pi}{12}$ where $n \in Z$.

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