Thay x bằng (x + y) / 2 và y bằng (x – y) / 2, suy ra:

sin ⁡ ( x ) + sin ⁡ ( y ) = 2 sin ⁡ ( x + y 2 ) cos ⁡ ( x − y 2 ) {\displaystyle \sin(x)+\sin(y)=2\sin \left({\frac {x+y}{2}}\right)\cos \left({\frac {x-y}{2}}\right)\;} sin ⁡ ( x ) − sin ⁡ ( y ) = 2 cos ⁡ ( x + y 2 ) sin ⁡ ( x − y 2 ) {\displaystyle \sin(x)-\sin(y)=2\cos \left({\frac {x+y}{2}}\right)\sin \left({x-y \over 2}\right)\;} cos ⁡ ( x ) + cos ⁡ ( y ) = 2 cos ⁡ ( x + y 2 ) cos ⁡ ( x − y 2 ) {\displaystyle \cos(x)+\cos(y)=2\cos \left({\frac {x+y}{2}}\right)\cos \left({\frac {x-y}{2}}\right)\;} cos ⁡ ( x ) − cos ⁡ ( y ) = − 2 sin ⁡ ( x + y 2 ) sin ⁡ ( x − y 2 ) {\displaystyle \cos(x)-\cos(y)=-2\sin \left({x+y \over 2}\right)\sin \left({x-y \over 2}\right)\;}