allery$\sin(A + B) = $
A$\sin A + \sin B$
B$\sin A \cos B - \cos A \sin B$
C$\sin A \cos B + \cos A \sin B$
D$\cos A \cos B - \sin A \sin B$
Answer & Solution
Correct answer: C. $\sin A \cos B + \cos A \sin B$
Angle-sum formula for sine: $\sin(A + B) = \sin A \cos B + \cos A \sin B$.
Companion: $\sin(A - B) = \sin A \cos B - \cos A \sin B$ (option C — common trap, the sine of the *difference*).
For cosine: $\cos(A \pm B) = \cos A \cos B \mp \sin A \sin B$ (sign flips inside vs outside, option D is $\cos(A+B)$).
Sine is not linear in its argument: $\sin(A+B) \neq \sin A + \sin B$ generally.
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