# Trigonometric Identity Proofs

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$\sin { \left( A+B \right) } =\sin { \left( A \right) } \cos { \left( B \right) } +\cos { \left( A \right) } \sin { \left( B \right) }$

A proof related to this identity [sin(A+B)] can be found here: https://www.youtube.com/watch?v=4K6xr8hjkTw&index=2&list=PLFM03zQeSz2MVj_4R9SZifMTL0re19LhK

$\sin { \left( A-B \right) } =\sin { \left( A \right) } \cos { \left( B \right) } -\cos { \left( A \right) } \sin { \left( B \right) }$

A proof related to this identity [sin(A-B)] can be found here: https://www.youtube.com/watch?v=sTOnQK7NfD0&index=3&list=PLFM03zQeSz2MVj_4R9SZifMTL0re19LhK

$\cos { \left( A+B \right) } =\cos { \left( A \right) } \cos { \left( B \right) } -\sin { \left( A \right) } \sin { \left( B \right) }$

A proof related to this identity [cos(A+B)] can be found here: https://www.youtube.com/watch?v=-n6h6-CT0-0&list=PLFM03zQeSz2MVj_4R9SZifMTL0re19LhK&index=4

$\cos { \left( A-B \right) } =\cos { \left( A \right) } \cos { \left( B \right) } +\sin { \left( A \right) } \sin { \left( B \right) }$

A proof related to this identity [cos(A-B)] can be found here: https://www.youtube.com/watch?v=gDOGT6NcD60&index=5&list=PLFM03zQeSz2MVj_4R9SZifMTL0re19LhK

$\tan { \left( A+B \right) } =\frac { \tan { \left( A \right) } +\tan { \left( B \right) } }{ 1-\tan { \left( A \right) } \tan { \left( B \right) } }$

A proof related to this identity [tan(A+B)] can be found here: https://www.youtube.com/watch?v=enSr4H1uCA4&list=PLFM03zQeSz2MVj_4R9SZifMTL0re19LhK&index=6

$\tan { \left( A-B \right) } =\frac { \tan { \left( A \right) } -\tan { \left( B \right) } }{ 1+\tan { \left( A \right) } \tan { \left( B \right) } }$

A proof related to this identity [tan(A-B)] can be found here: https://www.youtube.com/watch?v=SOkmA38B9kc&list=PLFM03zQeSz2MVj_4R9SZifMTL0re19LhK&index=7