If $\frac{3+i \sin \theta}{4-i \cos \theta}, \theta \in[0,2 \pi],$ is a real number, then an argument of $\sin \theta+\mathrm{i} \cos \theta$ is
If $\frac{3+i \sin \theta}{4-i \cos \theta}, \theta \in[0,2 \pi],$ is a real number, then an argument of $\sin \theta+\mathrm{i} \cos \theta$ is
- [JEE MAIN 2020]
- A
$-\tan ^{-1}\left(\frac{3}{4}\right)$
- B
$\tan ^{-1}\left(\frac{4}{3}\right)$
- C
$\pi-\tan ^{-1}\left(\frac{4}{3}\right)$
- D
$\pi-\tan ^{-1}\left(\frac{3}{4}\right)$
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