$\cos(\alpha-\beta)=\cos\alpha\cos\beta+\sin\alpha\sin\beta$
$\sin\alpha=\cos(\fracπ2-\alpha);\ \cos\alpha=\sin(\frac2π-\alpha)$
$$ \sin(\alpha+\beta)=\sin\alpha\cos\beta+\cos\alpha\sin\beta $$
$$ ⁍ $$
$$ \sin(\alpha+\beta)+\sin(\alpha-\beta)=2\sin\alpha\cos\beta $$
$$ \sin(\alpha+\beta)-\sin(\alpha-\beta)=2\cos\alpha\sin\beta $$