JEE Advanced Mathematics Question (2024) — Solution

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