If and are acute angles such that , then what is the maximum value of ? यदि A और B इस प्रकार के न्यून कोण हैं कि , तो का अधिकतम मान क्या है ?

Explanation: 1. Simplify the constraint: We are given . Dividing by 2, we get: 2. Express the product in terms of : We want to maximize . Substituting : Since , the expression becomes: 3. Use the double-angle identity: Recall the identity , which implies : 4. Find the maximum value: The maximum value of the sine function is . Therefore, the maximum value of is (which occurs when , or ). Final Answer: The maximum value of is . The correct option is (a) .

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NDA 2026 — Mathematics PYQ

NDA | Mathematics | 2026

If $A$ and $B$ are acute angles such that $2 A + 2 B = π$ , then what is the maximum value of $sin A \cdot sin B$ ?

यदि A और B इस प्रकार के न्यून कोण हैं कि $2 A + 2 B = π$ , तो $sin A \cdot sin B$ का अधिकतम मान क्या है ?

Choose the correct answer: