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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

The relation ^ -1 ((1 + x)/(1 - x)) = (π)/(4) + ^ -1 x holds true...

The relation tan⁡−1(1+x1−x)=π4+tan⁡−1x\tan^{-1} \left(\dfrac{1 + x}{1 - x}\right) = \dfrac{\pi}{4} + \tan^{-1} x holds true for all

Options

  1. Ax∈Rx \in \mathbb{R}
  2. Bx∈(−∞,1)x \in ( - \infty, 1 )
  3. Cx∈(−1,∞)x \in ( - 1, \infty )
  4. Dx∈(−∞,2)x \in ( - \infty, 2 )

Correct answer

B. x∈(−∞,1)x \in ( - \infty, 1 )

Step-by-step solution

Given, tan⁡−1(1+x1−x)=π4+tan⁡−1x\tan^{-1} \left(\dfrac{1 + x}{1 - x}\right) = \dfrac{\pi}{4} + \tan^{-1} x

RHS =π4+tan⁡−1x=tan⁡−11+tan⁡−1x= \dfrac{\pi}{4} + \tan^{-1} x = \tan^{-1} 1 + \tan^{-1} x

=tan⁡−1(1+x1−x),if= \tan^{-1} \left(\dfrac{1 + x}{1 - x}\right), if x < 1<br/><br/><br /><br />∴ x \in ( - ∞,1)\infty,1 )
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