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NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Trigonometric Equations

NDA 2021 · Mathematics · Trigonometric Equations

The value of x , satisfying the equation _ x x=1 , where 0 < x <...

The value of xx, satisfying the equation log⁡cos⁡xsin⁡x=1\log _{\cos x} \sin x=1, where 0<x<π20 < x < \frac{\pi}{2}, is

Options

  1. Aπ12\frac{\pi}{12}
  2. Bπ3\frac{\pi}{3}
  3. Cπ4\frac{\pi}{4}
  4. Dπ6\frac{\pi}{6}

Correct answer

C. π4\frac{\pi}{4}

Step-by-step solution

log⁡cos⁡xsin⁡x=1⇒log⁡sin⁡xlog⁡cos⁡x=1\begin{aligned} & \log _{\cos x} \sin x=1 \\ & \Rightarrow \frac{\log \sin x}{\log \cos x}=1\end{aligned} For x=π4,log⁡sin⁡π4log⁡cos⁡π4=log⁡(12)log⁡(12)=1x=\frac{\pi}{4}, \frac{\log \sin \frac{\pi}{4}}{\log \cos \frac{\pi}{4}}=\frac{\log \left(\frac{1}{\sqrt{2}}\right)}{\log \left(\frac{1}{\sqrt{2}}\right)}=1.
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