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JEE Main
Exam
JEE Main
Subject
Mathematics
Chapter
Inverse Trigonometric Functions

JEE Main · Mathematics · Inverse Trigonometric Functions

If ^ - 1 (tan(π)/(4)) - ^ - 1 (3)/(x) = (π)/(6) , then x & is a...

If sin⁡−1(tanπ4)−sin⁡−13x=π6\sin^{- 1}\left(tan\dfrac{π}{4}\right) - \sin^{- 1}\sqrt{\dfrac{3}{x}} = \dfrac{π}{6}, then xx& is a root of the equation

Options

  1. Ax2−x−6=0x^{2} - x - 6 = 0
  2. Bx2+x−6=0x^{2} + x - 6 = 0
  3. Cx2−x−12=0x^{2} - x - 12 = 0
  4. Dx2+x−12=0x^{2} + x - 12 = 0

Correct answer

C. x2−x−12=0x^{2} - x - 12 = 0

Step-by-step solution

sin⁡−1(1)−π6=sin⁡−13x\sin^{- 1}\left(1\right) - \dfrac{π}{6} = \sin^{- 1}\sqrt{\dfrac{3}{x}}

π2−π6=sin⁡−13x\dfrac{π}{2} - \dfrac{π}{6} = \sin^{- 1}\sqrt{\dfrac{3}{x}}

3x=32\sqrt{\dfrac{3}{x}} = \dfrac{3}{2}

⇒x=4⇒ x = 4

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