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NDA 2014
Exam
NDA
Year
2014
Subject
Mathematics
Chapter
Inverse Trigonometric Functions

NDA 2014 · Mathematics · Inverse Trigonometric Functions

Consider the following statements: 1. ^ -1 1+ ^ -1 (0.5)=π / 2 2. ^...

Consider the following statements: 1. tan⁡−11+tan⁡−1(0.5)=π/22.sin⁡−1(1/3)+cos⁡−1(1/3)=π/2\tan ^{-1} 1+\tan ^{-1}(0.5)=\pi / 2 2. \sin ^{-1}(1 / 3)+\cos ^{-1}(1 / 3)=\pi / 2 Which of the above statements is/are correct?

Options

  1. A1 only
  2. B2 only
  3. CBoth 1 and 2
  4. DNeither 1 nor 2

Correct answer

B. 2 only

Step-by-step solution

1. tan⁡−11+tan⁡−1(0.5)=π2\tan ^{-1} 1+\tan ^{-1}(0.5)=\frac{\pi}{2}. It is not true. 2. sin⁡−1\sin ^{-1}\left(\frac{1}{3}\right)+\cos ^{-1}(13)=π2\left(\frac{1}{3}\right)=\frac{\pi}{2} It is true because sin⁡−1x+cos⁡−1x=π2\sin ^{-1} x+\cos ^{-1} x=\frac{\pi}{2}.
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