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JEE Advanced2025MathematicsInverse Trigonometric FunctionsActual

The total number of real solutions of the equation = ⁻¹(2 )- 1 2 ⁻¹ ( 6 9+ ^2 ) is (Here, the inverse trigonometric functions ⁻¹ x and ⁻¹ x assume values in [- 2 , 2 ] and (- 2 , 2 ) , respectively.)

Options

  1. A1
  2. B2
  3. C3
  4. D5

Correct answer

C. 3

Step-by-step solution

Let = 1 2 ⁻¹ ( 6 9+ ^2 ) aligned & = ⁻¹(2 )- & + = ⁻¹(2 ) & ( + )=2 & + 1- =2 ....(1) & 2 = 6 9+ ^2 = 2 1+ ^2 & 3 +3 ^2 =9 + ^2 & 3( -3 )= ( -3 ) & = 3 or =3 aligned aligned & Case-I : =3 & + 3 1- ^2 3 =2 aligned =0, 2 3 =1- ^2 3 =1,-1 =0,-1,1 aligned & Case-II : = 3 & + 3 -2 =2 aligned

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