The most general value of theta which satisfi | vedclass

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(D) Given equations are $\sin 	heta = -\frac{1}{2}$ and $	an 	heta = \frac{1}{\sqrt{3}}$.For $\sin 	heta = -\frac{1}{2}$,$	heta$ lies in the $III

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None of these

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(D) Given equations are $\sin 	heta = -\frac{1}{2}$ and $	an 	heta = \frac{1}{\sqrt{3}}$.For $\sin 	heta = -\frac{1}{2}$,$	heta$ lies in the $III$ or $IV$ quadrant.For $	an 	heta = \frac{1}{\sqrt{3}}$,$	heta$ lies in the $I$ or $III$ quadrant.Both equations are satisfied when $	heta$ is in the $III$ quadrant.The principal value in the $III$ quadrant is $	heta = \pi + \frac{\pi}{6} = \frac{7\pi}{6}$.The general solution for $	heta$ is $2n\pi + \frac{7\pi}{6}$ where $n \in \mathbb{Z}$.Since this value is not present in the given options,the correct choice is $(d)$.

The most general value of $\theta$ which satisfies both the equations $\sin \theta = -\frac{1}{2}$ and $\tan \theta = \frac{1}{\sqrt{3}}$ is:

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