JEE Mains · Maths · STD 12 - 5. continuity and differentiation
The value of \(\log _{ e } 2 \frac{ d }{ dx }\left(\log _{\cos x } \operatorname{cosec} x \right)\) at \(x=\frac{\pi}{4}\) is.
- A \(-2 \sqrt{2}\)
- B \(2 \sqrt{2}\)
- C \(-4\)
- D \(4\)
Answer & Solution
Correct Answer
(D) \(4\)
Step-by-step Solution
Detailed explanation
\(\log _{e} 2 \frac{d}{d x}\left(\log _{\cos x} \operatorname{cosec} x\right)\) Let, \(y=\log _{\cos x} \operatorname{cosec} x\) \(y=-\frac{\ln (\sin x)}{\ln (\cos x)}\) \(\frac{d y}{d x}=-\frac{[\cot x \cdot \ln (\cos x)+\tan x \cdot \ln (\sin x)]}{(\ln (\cos x))^{2}}\)…
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