Find the general solutions of the following equations: 2x= 3 2 - Vidyadip

Question

Find the general solutions of the following equations: $\sin2\text{x}=\frac{\sqrt{3}}{2}$

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Answer

We have, $\sin2\text{x}=\frac{\sqrt{3}}{2}$ $\Rightarrow\sin2\theta=\sin\Big(\frac{\pi}{3}\Big)$ $\Rightarrow2\theta=\text{n}\pi+(-1)^{\text{n}}\frac{\pi}{3},\text{n}\in\text{z}$ $\theta=\frac{\text{n}\pi}{2}+(-1)^{n}\frac{\pi}{6},\text{n}\in\text{z}$

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