Sum of sines / cosine in terms of products

Values of sin(A+B) and cos(A+B) in terms of their product is given by

$\displaystyle \sin { A } +\sin { B } =2\sin { \left( \frac { A+B }{ 2 } \right) } \cos { \left( \frac { A-B }{ 2 } \right) }$
$\displaystyle \sin { A } -\sin { B } =2\cos { \left( \frac { A+B }{ 2 } \right) } \sin { \left( \frac { A-B }{ 2 } \right) }$
$\displaystyle \cos { A } +\cos { B } =2\cos { \left( \frac { A-B }{ 2 } \right) } \cos { \left( \frac { A-B }{ 2 } \right) }$
$\displaystyle \cos { A } -\cos { B } =2\cos { \left( \frac { A+B }{ 2 } \right) } \cos { \left( \frac { B-A }{ 2 } \right) }$
$\displaystyle \tan { A } +\tan { B } =\frac { \sin { \left( A+B \right) } }{ \cos { A } \cos { B } } \quad where\quad A,B\neq n\pi +\frac { \pi }{ 2 }$
$\displaystyle \tan { A } -\tan { B } =\frac { \sin { \left( A-B \right) } }{ \cos { A } \cos { B } } \quad where\quad A,B\neq n\pi +\frac { \pi }{ 2 }$
$\displaystyle \cot { A } +\cot { B } =\frac { \sin { \left( A+B \right) } }{ \sin { A } \sin { B } } \quad where\quad A,B\neq n\pi \quad n=z$
$\displaystyle \cot { A } -\cot { B } =\frac { \sin { \left( B-A \right) } }{ \sin { A } \sin { B } } \quad where\quad A,B\neq n\pi \quad n=z$