Question

The general solution of the equation $\sin x=\frac{\sqrt{3}}{2}$ is x=

• A. 2nπ±π3
• B. nπ+(-1)nπ3
• C. nπ ± π6

Answer 1

The correct option is B nπ+(-1)nπ3

The general solution to the equation
$\sin x=\sin \alpha$, where $\alpha \in [-\frac{\pi }{2},\frac{\pi }{2}]$ is
$x=n\pi +(-1{)}^n\alpha$

Here, $\sin x=\frac{\sqrt{3}}{2}$
$\Rightarrow \sin x=\sin \frac{\pi }{3}$.
Also, $\frac{\pi }{3}\in [-\frac{\pi }{2},\frac{\pi }{2}]$

Hence, the general solution of the equation is $x=n\pi +(-1{)}^n\frac{\pi }{3}$