Question
State whether the following are true or false. Justify your answer.$\sin (\text{A}+\text{B})=\sin \text{A}+\sin\text{B}.$
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Answer
$\sin (\text{A}+\text{B})=\sin \text{A}+\sin \text{B}$False, suppose $\text{A}=30^\circ, \text{B}=60^\circ$ because $\sin(\text{A}+\text{B})=\sin 90^\circ=1$ $\sin \text{A}+\sin \text{B}=\frac{1}{2}+\frac{\sqrt{3}}{2}\neq1$
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