\(\color{blue}\sin\text{A} + \sin \text{B} = 2\sin\dfrac{1}{2}\text{(A + B)}\cos \dfrac{1}{2}\text{(A − B)}\)
\(\color{blue}\sin\text{A} \:-\: \sin\text{B} = 2\cos\dfrac{1}{2}\text{(A + B)}\sin \dfrac{1}{2}\text{(A − B)}\)
\(\color{blue}\cos \text{A} + \cos \text{B} = 2\cos \dfrac{1}{2}\text{(A + B)}\cos \dfrac{1}{2}\text{(A − B)}\)
\(\color{blue}\cos \text{A} \:-\:\cos \text{B} = -2\sin \dfrac{1}{2}\text{(A + B)}\sin \dfrac{1}{2}\text{(A − B)}\)