Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202616 April 2026Evening ShiftMathematicsInverse Trigonometric FunctionsActual

If ( ⁻¹x)^2 + ( ⁻¹x)^2 = 5 ^2 8 , then the value of x is equal to...

Options

  1. A-1
  2. B-2
  3. C1
  4. 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

Practice Inverse Trigonometric Functions on Quantrex Academy →

More from Inverse Trigonometric Functions

If y = ⁻¹ ( 1+x^3 + 1-x^3 1+x^3 - 1-x^3 ) then dy dx = 2026If X = ⁻¹ [2 (2 ⁻¹ 1 2 ) ] + ⁻¹ [ ( 7 6 ) ] and Y = ⁻¹ [ ( 11 6 ) ] + ⁻¹ [ ( 4 3 ) ] then the value of 2X - Y is: 2026The value of the expression ⁻¹ ( 7 6 ) + ⁻¹ ( 22 3 ) + ⁻¹ ( 4 5 ) is: 2026Which of the following is the simplest form of the expression ⁻¹ ( 1+x^2 - 1 x ) where x 0 2026If ⁻¹ x + ⁻¹ y = 2 , then x^2 is equal to 2026⁻¹ ( 1 1 + 1 2 ) + ⁻¹ ( 1 1 + 2 3 ) + + ⁻¹ ( 1 1 + n(n+1) ) = 2026The second order derivative of ⁻¹(4x^3 - 3x) with respect to ⁻¹(2x^2 - 1) , where 1 2 < x < 1 is 2026If 2 ⁻¹x - 3 ⁻¹x = 4 , then 2 ⁻¹x + 3 ⁻¹x = 2026 Full Inverse Trigonometric Functions list All MHT CET PYQs