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

n π + (- 1)^{n} (\frac{- π}{6}), n \in Z

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n π \pm (- 1)^{n} \frac{2 π}{3}, n \in Z

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n π \pm \frac{π}{3}, n \in Z

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n π \pm (- 1)^{n} (\frac{- π}{6}), n \in Z

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Solution

The correct option is A $n π + (- 1)^{n} (\frac{- π}{6}), n \in Z$
$2 sin x + 1 = 0 \Rightarrow sin x = \frac{- 1}{2} \Rightarrow sin x = sin (\frac{- π}{6}) \Rightarrow x = n π + (- 1)^{n} (\frac{- π}{6}), n \in Z$

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