Ucale

# T-Ratios of the Sum of three or more Angles

Values of Trigonometrical functions for the sum of three or more than three angles i.e. sin(A+B+C) , cos (A+B+C)…….

1. $\displaystyle \sin { \left( A+B+C \right) } =\sin { A } \cos { B } \cos { C }$+$\displaystyle Â \cos { A } \sin { B } \sin { C }$+$\displaystyle \cos { A } \cos { B } \sin { C }$$\displaystyle \sin { A } \sin { B } \sin { C }$
or$\displaystyle \sin { \left( A+B+C \right) } =\cos { A } \cos { B } \cos { C }$ x $\displaystyle (\tan { A } +\tan { B } +\tan { C } -\tan { A } \tan { B } \tan { C } )$
2. $\displaystyle \cos { \left( A+B+C \right) } =\cos { A } \cos { B } \cos { C }$$\displaystyle \sin { A } \sin { B } \cos { C }$$\displaystyle \sin { A } \cos { B } \sin { C }$$\displaystyle \cos { A } \sin { B } \sin { C }$
3. $\displaystyle \tan { \left( A+B+C \right) }$ =$\displaystyle\frac { \tan { A } +\tan { B } +\tan { C } -\tan { A } \tan { B } \tan { C } }{ 1-\tan { A } \tan { B } -\tan { B } \tan { C } -\tan { C } \tan { A } }$
February 22, 2019
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