MHT CET202616 April 2026Evening ShiftMathematicsInverse Trigonometric FunctionsActual
If ( ⁻¹x)^2 + ( ⁻¹x)^2 = 5 ^2 8 , then the value of x is equal to...
Options
- A-1
- B-2
- C1
- D2
Correct answer
A. -1
Step-by-step solution
Let ⁻¹x = t . Then ⁻¹x = 2 - t . Substituting in the given equation: t^2 + ( 2 - t )^2 = 5 ^2 8 2t^2 - t + ^2 4 - 5 ^2 8 = 0 2t^2 - t - 3 ^2 8 = 0 16t^2 - 8 t - 3 ^2 = 0 (4t - 3 )(4t + ) = 0 t = 3 4 or t = - 4 Since the principal value branch of ⁻¹x is (- 2 , 2 ) , t = 3 4 is rejected. Therefore, ⁻¹x = - 4 x = (- 4 ) = -1 Answer: -1