Rumus umum jumlah sinus adalah

$\sin\alpha+\sin\beta=2\sin\frac{1}{2}\left(\alpha+\beta\right)\cos\frac{1}{2}\left(\alpha-\beta\right)$

Dengan demikian,

$\sin23\degree+\sin27\degree=2\sin\frac{1}{2}\left(23\degree+27\degree\right)\cos\frac{1}{2}\left(23\degree-27\degree\right)$

$=2\sin\frac{1}{2}\left(50\degree\right)\cos\frac{1}{2}\left(-4\degree\right)$

$=2\sin25\degree\cos\left(-2\degree\right)$

Ingat hubungan $\cos\left(-\theta\right)=\cos\theta$ sehingga

$=2\sin25\degree\cos2\degree$