- A$2\text{n}\pi\pm\frac{\pi}{3},\text{n}\in\text{Z}$
- B$\text{n}\pi\pm\frac{\pi}{3},\text{n}\in\text{Z}$
- C$\text{n}\pi\pm\frac{\pi}{6},\text{n}\in\text{Z}$
- D$2\text{n}\pi\pm\frac{\pi}{6},\text{n}\in\text{Z}$
Solution:
Given:
$\Rightarrow\sin^2\text{x}=1$
$\Rightarrow\sin^2\text{x}=\frac{1}{4}$
$\Rightarrow\sin\text{x}=\frac{1}{2}$ or $\sin\text{x}=-\frac{1}{2}$
$\Rightarrow\sin\text{x}=\sin\frac{\pi}{6}$ or $\sin\text{x}=\sin\Big(-\frac{\pi}{6}\Big)$
$\Rightarrow\text{x}=\text{n}\pi+(-1)^\text{n}\frac{\pi}{6},\text{n}\in\text{Z}$ or $\text{n}\pi+(-1)^\text{n}\Big(-\frac{\pi}{6}\Big),\text{n}\in\text{Z}$
$\Rightarrow\text{x}=\text{n}\pi\pm\frac{\pi}{6},\text{n}\in\text{Z}$
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