Question

If \[4 \sin^2 x = 1\], then the values of x are

 

Options

• \[2 n\pi \pm \frac{\pi}{3}, n \in Z\]

• \[n\pi \pm \frac{\pi}{3}, n \in Z\]

   

• \[n\pi \pm \frac{\pi}{6}, n \in Z\]

• \[2 n\pi \pm \frac{\pi}{6}, n \in Z\]

Answer 1

\[2 n\pi \pm \frac{\pi}{6}, n \in Z\]
Given:
\[4 \sin^2 x = 1\]
\[ \Rightarrow \sin^2 x = \frac{1}{4}\]
\[ \Rightarrow \sin x = \frac{1}{2}\text{ or }\sin x = - \frac{1}{2}\]
\[ \Rightarrow \sin x = \sin \frac{\pi}{6}\text{ or }\sin x = \sin \left( - \frac{\pi}{6} \right)\]
\[ \Rightarrow x = n\pi + ( - 1 )^n \frac{\pi}{6}, n \in Z\text{ or }x = n\pi + ( - 1 )^n \left( - \frac{\pi}{6} \right), n \in Z\]
\[ \Rightarrow x = n\pi \pm \frac{\pi}{6}, n \in Z\]