The complete solution set of the equation \( 1+2 \operatorname{cose...

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The complete solution set of the equation \( 1+2 \operatorname{cosec} x=-\frac{\sec ^{2} \frac{x}{2}}{2} \) is
\( \mathrm{P} \)
(A) \( 2 \mathrm{n} \pi-\frac{\pi}{2}, \mathrm{n} \in \mathrm{I} \)
(B) \( \mathrm{n} \pi-\frac{\pi}{2}, \mathrm{n} \in \mathrm{I} \)
(C) \( 2 \mathrm{n} \pi+\frac{\pi}{2}, \mathrm{n} \in \mathrm{I} \)
(D) \( \mathrm{n} \pi+\frac{\pi}{2}, \mathrm{n} \in \mathrm{I} \)
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