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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Inverse Trigonometric Functions

NTA Abhyas 2020 · Mathematics · Inverse Trigonometric Functions

If x takes all permissible negative values, then ^ -1 x is equal to

If xx takes all permissible negative values, then sin⁡−1x\sin^{-1} x is equal to

Options

  1. A−cos⁡−11−x2- \cos^{-1} \sqrt{1 - x^{2}}
  2. Bcos⁡−1x2−1\cos^{-1} \sqrt{x^{2} - 1}
  3. Cπ−cos⁡−11−x2\pi - \cos^{-1} \sqrt{1 - x^{2}}
  4. Dcos⁡−11−x2\cos^{-1} \sqrt{1 - x^{2}}

Correct answer

A. −cos⁡−11−x2- \cos^{-1} \sqrt{1 - x^{2}}

Step-by-step solution

Let x=−y,y>0x = - y, y > 0

∴sin⁡−1x=sin⁡−1(−y)∴ \sin^{-1} x = \sin^{-1} \left(-y\right)

=−sin−1y= {- sin}^{- 1} y

=−cos⁡−1= - \cos^{-1}\sqrt{1 - y^{2}}

=−cos⁡−11−x2= - \cos^{-1} \sqrt{1 - x^{2}}
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