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.)

Question

Quantrex Academy · Accepted Answer

Correct answer: C. 3

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

JEE Advanced Mathematics Question (2025) — Solution

Question

Options

Answer

Step-by-step solution