Question

General solutions of $x$ for which $2\sin x+1=0$ is :

• A. $n\pi +(-1{)}^n\left(\frac{-\pi }{6}\right),n\in Z$
• B. $n\pi \pm (-1{)}^n\frac{2\pi }{3},n\in Z$
• C. $n\pi \pm \frac{\pi }{3},n\in Z$
• D. $n\pi \pm (-1{)}^n\left(\frac{-\pi }{6}\right),n\in Z$

Answer 1

The correct option is A $n\pi +(-1{)}^n\left(\frac{-\pi }{6}\right),n\in Z$

$2\sin x+1=0\Rightarrow \sin x=\frac{-1}{2}\Rightarrow \sin x=\sin \left(\frac{-\pi }{6}\right)\Rightarrow x=n\pi +(-1{)}^n\left(\frac{-\pi }{6}\right),n\in Z$