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NDA 2022
Exam
NDA
Year
2022
Subject
Mathematics
Chapter
Inverse Trigonometric Functions

NDA 2022 · Mathematics · Inverse Trigonometric Functions

What is ^ -1 (cosec^ -1 2) equal to?

What is tan⁡−1cot⁡(cosec⁡−12)equalto?\tan ^{-1} \cot \left(\operatorname{cosec}^{-1}2\right) equal to?

Options

  1. Aπ8\frac{\pi}{8}
  2. Bπ6\frac{\pi}{6}
  3. Cπ4\frac{\pi}{4}
  4. Dπ3\frac{\pi}{3}

Correct answer

D. π3\frac{\pi}{3}

Step-by-step solution

tan⁡−1cot⁡(cosec⁡−12)=tan⁡−1(cot⁡π6)=tan⁡−13=π3\begin{aligned} & \tan ^{-1} \cot \left(\operatorname{cosec}^{-1} 2\right) \\ & =\tan ^{-1}\left(\cot \frac{\pi}{6}\right)=\tan ^{-1} \sqrt{3}=\frac{\pi}{3}\end{aligned}
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