Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202526 Apr 2025Evening ShiftMathematicsInverse Trigonometric FunctionsActual

Considering only the principal values of the inverse trigonometric functions, the value of ( ⁻¹ ( 3 5 )-2 ⁻¹ ( 2 5 ) ) is

Options

  1. A7 24
  2. B-7 24
  3. C5 24
  4. D-5 24

Correct answer

B. -7 24

Step-by-step solution

Let E = ( ⁻¹ ( 3 5 ) - 2 ⁻¹ ( 2 5 ) ) . Evaluate the inverse trigonometric expressions: Let = ⁻¹ ( 3 5 ) , so = 3 5 and = 3 4 . Let = ⁻¹ ( 2 5 ) , so = 2 5 and = 1 2 . Compute the double angle: Using (2 ) = 2 1 - ^2 , we obtain (2 ) = 2 1 2 1 - ( 1 2 )^2 = 4 3 . Apply the tangent subtraction formula: E = ( - 2 ) = - (2 ) 1 + (2 ) = 3 4 - 4 3 1 + 3 4 4 3 = - 7 12 2 = - 7 24 . Final result: - 7 24

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