Question
If A and B are acute angles such that 2A+2B= , then what is the maximum value of A B ?
NDA
Mathematics
Trigonometric Ratios & Identities
2026
NDA 2026 (Phase 1)
NDA Mathematics Question (2026) — Solution
Options
- A. 1 2
- B. 1 4
- C. 3 4
- D. 1
Answer
A. 1 2
Step-by-step solution
Given 2A + 2B = , which simplifies to A + B = 2 . Since A and B are acute angles, B = 2 - A. The expression to maximize is A B. Substituting B = 2 - A, we get A ( 2 - A ) = A A. Multiplying and dividing by 2, we obtain 2 A A 2 = 2A 2 . The maximum value of 2A is 1, which occurs when 2A = 2 , or A = 4 . Therefore, the maximum value of A B is 1 2 1 = 1 2 . Answer: 1 2
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