The sum of the solution of the equation \( \frac{\cos x}{1+\sin x}=...

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The sum of the solution of the equation \( \frac{\cos x}{1+\sin x}=|\tan 2 x|, x \in\left(\frac{-\pi}{2}, \frac{\pi}{2}\right)-\left\{\frac{\pi}{4},-\frac{\pi}{4}\right\} \) is:
\( \mathrm{P} \)
[JEE Main-2021 (August)]
WV
(a) \( \frac{\pi}{10} \)
(b) \( -\frac{11 \pi}{30} \)
(c) \( -\frac{7 \pi}{30} \)
(d) \( -\frac{\pi}{15} \)
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