NDA Mathematics Question (2025) — Solution

Step-by-step solution

Let A = ^ -1 9 A = 9 A = 1 9 Let B = cosec ^ -1 ( 41 4 ) cosec B = 41 4 B = 4 41 From this, B = 4 ( 41 )^2 - 4^2 = 4 41 - 16 = 4 5 Using the formula (A + B) = A + B 1 - A B : (A + B) = 1 9 + 4 5 1 - ( 1 9 ) ( 4 5 ) (A + B) = 5 + 36 45 45 - 4 45 (A + B) = 41 41 = 1 Since A, B (0, 2 ), we have A + B = 4 Answer: 4