Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
COMEDK2024MathematicsInverse Trigonometric FunctionsActual

If = ⁻¹ ( 5 4 ) and = ⁻¹ (- 2 3 ) then

Options

  1. A+ =- 7 12
  2. B3 =4
  3. C- = 7 12
  4. D4 =3

Correct answer

D. 4 =3

Step-by-step solution

The expression for is given by = ⁻¹( 5 4 ) . Since 5 4 is in the third quadrant, 5 4 = ( + 4 ) = 4 = 1 . Thus, = ⁻¹(1) = 4 . The expression for is given by = ⁻¹(- 2 3 ) . Since 2 3 = ( - 3 ) = - 3 = - 3 , we have - 2 3 = 3 . Thus, = ⁻¹( 3 ) = 3 . Checking the options: Option (1): + = 4 + 3 = 7 12 - 7 12 . Option (2): 3 = 3( 4 ) = 3 4 and 4 = 4( 3 ) = 4 3 . These are not equal. Option (3): - = 4 - 3 = - 12 7 12 . Option (4): 4 = 4( 4 ) = and 3 = 3( 3 ) = . Since 4 = 3 = , this option is correct. Answer: 4 =3

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 COMEDK PYQs