Answer
2 formulas differ in the sign of $\cos A\sin B$. While in $\sin (A-B)$, the sign is negative, in $\sin (A+B)$, the sign is positive.
2 formulas both contain $\sin A\cos B$ and $\cos A\sin B$. The sign of $\sin A\cos B$ in both formulas is also positive.
Work Step by Step
- Formula for $\sin(A-B)$
$$\sin(A-B)=\sin A\cos B-\cos A\sin B$$
- Formula for $\sin (A+B)$
$$\sin(A+B)=\sin A\cos B+\cos A\sin B$$
As shown above, the content of each formula is the same. Both $\sin (A-B)$ and $\sin (A+B)$ contain $\sin A\cos B$ and $\cos A\sin B$. The sign of $\sin A\cos B$ in both cases are alike, which is positive.
The only difference is the sign of $\cos A\sin B$.
- In $\sin (A-B)$, the sign of $\cos A\sin B$ is negative.
- In $\sin (A+B)$, the sign of $\cos A\sin B$ is positive.