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JEE MATHEMATICS MCQ: PROPERTIES OF TRIANGLES

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If sin⁡A+cos  B=a\sin A + cos\;B = a and sin⁡B+cos⁡A=b\sin B + \cos A = b, then sin⁡(A+B)\sin \left( {A + B} \right) is equal to
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Correct option: C
a2+b2−22\frac{{{a^2} + {b^2} - 2}}{2}
Option C (a2+b2−22\frac{{{a^2} + {b^2} - 2}}{2}) is correct because squaring and adding the given equations allows us to express sin⁡(A+B)\sin(A+B) in terms of aa and bb.

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