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)…….

$\displaystyle \sin { \left( A+B+C \right) } =\sin { A } \cos { B } \cos { C }$ + $\displaystyle \cos { A } \sin { B } \sin { C }$ + $\displaystyle \cos { A } \cos { B } \sin { C }$ – $\displaystyle \sin { A } \sin { B } \sin { C }$
or $\displaystyle \sin { \left( A+B+C \right) } =\cos { A } \cos { B } \cos { C }$ x $\displaystyle (\tan { A } +\tan { B } +\tan { C } -\tan { A } \tan { B } \tan { C } )$
$\displaystyle \cos { \left( A+B+C \right) } =\cos { A } \cos { B } \cos { C }$ – $\displaystyle \sin { A } \sin { B } \cos { C }$ – $\displaystyle \sin { A } \cos { B } \sin { C }$ – $\displaystyle \cos { A } \sin { B } \sin { C }$
$\displaystyle \tan { \left( A+B+C \right) }$ = $\displaystyle\frac { \tan { A } +\tan { B } +\tan { C } -\tan { A } \tan { B } \tan { C } }{ 1-\tan { A } \tan { B } -\tan { B } \tan { C } -\tan { C } \tan { A } }$

February 22, 2019

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