JEE Mains · Maths · STD 12 - 5. continuity and differentiation
If \(\mathrm{y}(\alpha)=\sqrt{2\left(\frac{\tan \alpha+\cot \alpha}{1+\tan ^{2} \alpha}\right)+\frac{1}{\sin ^{2} \alpha}}, \alpha \in\left(\frac{3 \pi}{4}, \pi\right)\) then \(\frac{d y}{d \alpha}\) at \(\alpha=\frac{5 \pi}{6}\) is
- A \(4\)
- B \(-\frac{1}{4}\)
- C \(\frac{4}{3}\)
- D \(-4\)
Answer & Solution
Correct Answer
(A) \(4\)
Step-by-step Solution
Detailed explanation
\(\mathrm{y}(\alpha)=\sqrt{2 \frac{(\tan \alpha+\cot \alpha)}{1+\tan ^{2} \alpha}+\frac{1}{\sin ^{2} \alpha}}, \alpha \in\left(\frac{3 \pi}{4}, \pi\right)\) \(=\frac{|\sin \alpha+\cos \alpha|}{|\sin \alpha|}=\frac{-(\sin \alpha+\cos \alpha)}{\sin \alpha}\) \(=-1-\cot \alpha\)…
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