Question : Which of the following options gives an expression equivalent to $\sin \ (A + B)$?
Option 1: $\cos\ A \cos\ B - \sin \ A \sin \ B$
Option 2: $\sin\ A \cos \ B + \cos\ A\ \sin \ B$
Option 3: $\cos \ A \cos\ B+\sin\ A \sin \ B$
Option 4: $\sin \ A \cos \ B - \cos \ A \sin \ B$
Correct Answer: $\sin\ A \cos \ B + \cos\ A\ \sin \ B$
Solution :
Given: $\sin \ (A + B)$
We know the formula, $\sin\ (A + B) = (\sin\ A \cos\ B + \cos\ A\ \sin\ B)$
Hence, the correct answer is $(\sin\ A \cos \ B + \cos \ A\ \sin \ B)$.
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