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NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Inverse Trigonometric Functions

NDA 2021 · Mathematics · Inverse Trigonometric Functions

The equation ^ -1 x- ^ -1 x=(π)/(6) has

The equation sin⁡−1x−cos⁡−1x=π6\sin ^{-1} x-\cos ^{-1} x=\frac{\pi}{6} has

Options

  1. Ano solution
  2. Bunique solution
  3. Ctwo solutions
  4. Dinfinite number of solutions

Correct answer

B. unique solution

Step-by-step solution

sin⁡−1x−cos⁡−1x=π6…\sin ^{-1} x-\cos ^{-1} x=\frac{\pi}{6} \ldots (i) We know that, sin⁡−1x+cos⁡−1x=π2…\sin ^{-1} x+\cos ^{-1} x=\frac{\pi}{2} \ldots (ii) On adding, sin⁡−1x=π3\sin ^{-1} x=\frac{\pi}{3}
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