JEE Advanced Mathematics Question (2026) — Solution

Step-by-step solution

For the first term, ^ -1 ( (-11)): The principal value branch of ^ -1 (x) is (0, ). Since the cotangent function is periodic with period , (-11) = (-11 + 4 ). Using 3.14, we have 4 12.56, so -11 + 4 1.56, which lies in the interval (0, ). Thus, ^ -1 ( (-11)) = 4 - 11. For the second term, 10 (2 ^ -1 ( 1 2 ) ): Since ^ -1 ( 1 2 ) = 4 , we get: 10 (2 4 ) = 10 ( 2 ) = 10(1) = 10. For the third term, 10 (2 ^ -1 (2)): Let = ^ -1 (2) ( ) = 2. Using the multiple angle formula (2 ) = 2 ( ) 1 + ^2( ) , we obtain: (2 ) = 2(2) 1 + 2^2 = 4 5 . Therefore, 10 (2 ^ -1 (2)) = 10 4 5 = 8. Adding the three evaluated terms together: (4 - 11) + 10 + 8 = 4 + 7. Answer: 4 + 7