\( \because \sin(\alpha+\beta)=|CD|/|OC|,|OC|=1 \)
\( \therefore \sin(\alpha+\beta)=|CD| \)
\( \because \angle OCE=\pi/2-\beta,\angle OCD=\pi/2-(\beta+\alpha) \)
\( \therefore \angle DCE=\alpha \)
\( \because |CD|=|CG|+|GD|=|CG|+|EF| \)
\( \therefore \sin(\alpha+\beta)=|CE|\cdot\cos\alpha+|OE|\cdot\sin\alpha \)
\( \therefore \sin(\alpha+\beta)=|OC|\cdot\sin\beta\cdot\cos\alpha+|OC|\cdot\cos\beta\cdot\sin\alpha \)
\( \therefore \sin(\alpha+\beta)=\sin\beta\cdot\cos\alpha+\cos\beta\cdot\sin\alpha \)

類似的
\( \because \cos(\alpha+\beta)=|OD|=|OF|-|GE| \)
\( \therefore \cos(\alpha+\beta)=|OE|\cdot\cos\alpha-|CE|\cdot\sin\alpha \)
\( \therefore \cos(\alpha+\beta)=\cos\beta\cdot\cos\alpha-\sin\beta\cdot\sin\alpha \)