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NDA 2012
Exam
NDA
Year
2012
Subject
Mathematics
Chapter
Inverse Trigonometric Functions

NDA 2012 · Mathematics · Inverse Trigonometric Functions

What is the value of ^2 ^ -1 ((5)/(11))?

What is the value of $\sec ^2 \tan ^{-1} \left(\frac{5}{11}\right)?

Options

  1. A121/96
  2. B217/921
  3. C146/121
  4. D267/121

Correct answer

B. 217/921

Step-by-step solution

sec⁡2(tan⁡−1(511))1+tan⁡2(tan⁡−1(511))1+[tan⁡{tan⁡−1(511)2}]1+25121121+25121=146121.\begin{aligned} & \sec ^2\left(\tan ^{-1}\left(\frac{5}{11}\right)\right) \\ & 1+\tan ^2\left(\tan ^{-1}\left(\frac{5}{11}\right)\right) \\ & 1+\left[\tan \left\{\tan ^{-1}\left(\frac{5}{11}\right)^2\right\}\right] \\ & 1+\frac{25}{121} \quad \frac{121+25}{121}=\frac{146}{121}.\end{aligned}
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