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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Application of Derivatives

NDA 2023 · Mathematics · Application of Derivatives

Paragraph: Let x=( ^2 A+ A+1)/( A) where 0 Question: At what value...

Paragraph: Let x=sin⁡2A+sin⁡A+1sin⁡Ax=\frac{\sin ^2 A+\sin A+1}{\sin A} where 0<A≤π20 < A \leq \frac{\pi}{2}
Question: At what value of AA does xx attain the minimum value?

Options

  1. Aπ6\frac{\pi}{6}
  2. Bπ4\frac{\pi}{4}
  3. Cπ3\frac{\pi}{3}
  4. Dπ2\frac{\pi}{2}

Correct answer

D. π2\frac{\pi}{2}

Step-by-step solution

For minimum value, sin⁡A+1sin⁡A=2sin⁡2A−2sin⁡A+1=0(sin⁡A−1)2=0sin⁡A=1⇒∴A=π2\sin A+\frac{1}{\sin A}=2\sin ^2 A-2 \sin A+1=0(\sin A-1)^2=0\sin A=1 \Rightarrow \therefore A=\frac{\pi}{2}
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