If ${{3 + i\sin \theta } \over {4 - i\cos \theta }}$, $\theta $ $ \in $ [0, 2$\theta $], is a real number, then an argument of sin$\theta $ + icos$\theta $ is :

Question

If ${{3 + i\sin \theta } \over {4 - i\cos \theta }}$, $\theta $ $ \in $ [0, 2$\theta $], is a real number, then an argument of
sin$\theta $ + icos$\theta $ is :

$\pi - {\tan ^{ - 1}}\left( {{3 \over 4}} \right)$

$ - {\tan ^{ - 1}}\left( {{3 \over 4}} \right)$

${\tan ^{ - 1}}\left( {{4 \over 3}} \right)$

$\pi - {\tan ^{ - 1}}\left( {{4 \over 3}} \right)$

Solution

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