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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 the trigonometric equation ^ -1 x = 2 ^ -1 a has a solution,...

If the trigonometric equation tan⁡−1x=2sin⁡−1a\tan^{-1} x = 2\sin^{-1} a has a solution, then the complete set of values of aa is

Options

  1. A12<∣a∣<12\dfrac{1}{2} < \left|a\right| < \dfrac{1}{\sqrt{2}}
  2. Ball real values of aa
  3. C∣a∣<12\left|a\right| < \dfrac{1}{2}
  4. D∣a∣<12\left|a\right| < \dfrac{1}{\sqrt{2}}

Correct answer

D. ∣a∣<12\left|a\right| < \dfrac{1}{\sqrt{2}}

Step-by-step solution

∵ \tan^{-1} x \in \left(- \dfrac{\pi}{2}, \dfrac{\pi}{2}\right)
∴−∴ -\dfrac{\pi}{2}< 2\sin^{-1} a < \dfrac{\pi}{2}<br/><br />- \dfrac{\pi}{4}<sin⁡−1a<< \sin^{-1} a <\dfrac{\pi}{4}⇒a∈(−12,12)⇒ a \in \left(- \dfrac{1}{2}, \dfrac{1}{2}\right)
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