Answer
$ sin (\alpha-\beta)=sin \alpha cos\beta- cos\alpha sin\beta$
Work Step by Step
Use the addition formula for cosine and sine identities.
$ cos (\alpha+\beta)= cos \alpha cos\beta- sin \alpha sin\beta$
Change $\alpha$ with $(\pi/2-\alpha)$
$ cos [(\pi/2-\alpha)+\beta]= cos (\pi/2-\alpha) cos\beta- sin (\pi/2-\alpha) sin\beta$
$ cos [\pi/2-(\alpha-\beta)]= cos (\pi/2-\alpha) cos\beta- sin (\pi/2-\alpha) sin\beta$
Hence, $ sin (\alpha-\beta)=sin \alpha cos\beta- cos\alpha sin\beta$