The value of \( \log _{e} 2 \frac{d}{d x}\left(\log _{\cos x} \operatorname{cosec} x\right) \) a...

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The value of \( \log _{e} 2 \frac{d}{d x}\left(\log _{\cos x} \operatorname{cosec} x\right) \) at \( x=\frac{\pi}{4} \) is
(a) \( -2 \sqrt{2} \)
(b) \( 2 \sqrt{2} \)
(c) -4
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