COMEDK2024MathematicsInverse Trigonometric FunctionsActual
If = ⁻¹ ( 5 4 ) and = ⁻¹ (- 2 3 ) then
Options
- A+ =- 7 12
- B3 =4
- C- = 7 12
- 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