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JEE Main202522 Jan 2025Morning ShiftMathematicsInverse Trigonometric FunctionsActual

Using the principal values of the inverse trigonometric functions, the sum of the maximum and the minimum values of 16 ( ( ⁻¹ x )^2+ ( cosec ⁻¹ x )^2 ) is :

Options

  1. A24 ^2
  2. B22 ^2
  3. C31 ^2
  4. D18 ^2

Correct answer

B. 22 ^2

Step-by-step solution

aligned & 16 ( ⁻¹ x )^2+ ( cosec ⁻¹ x )^2 & Sec ⁻¹ x=a [0, ]- 2 & cosec ⁻¹ x= 2 -a & =16 [a^2+ ( 2 -a )^2 ]=16 [2 a^2- a+ ^2 4 ] & ]_ a= =16 [2 ^2- ^2+ 2 4 ]=20 ^2 & ]_ a= 4 =16 [ 2 ^2 16 - ^2 4 + ^2 4 ]=2 ^2 & Sum =22 ^2 aligned

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