MandysNotes

Tuesday, 13 November 2012 19:19

Addition Formulae

By  Gideon
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\[ {\color{Goldenrod}\sin}\ \left( {\color{MidnightBlue}z_{1}} + {\color{MidnightBlue}z_{2}} \right) = {\color{Goldenrod}\sin}\ {\color{MidnightBlue}z_{1}} \ {\color{Blue}\cos}\ {\color{MidnightBlue}z_{2}} \ + \ {\color{Blue}\cos}\ {\color{MidnightBlue}z_{1}}\ {\color{Goldenrod}\sin}\ {\color{MidnightBlue}z_{2}} \ \]


\[ {\color{Blue}\cos}\ \left( {\color{MidnightBlue}z_{1}} + {\color{MidnightBlue}z_{2}} \right) = {\color{Blue}\cos}\ {\color{MidnightBlue}z_{1}} \ {\color{Blue}\cos}\ {\color{MidnightBlue}z_{2}} \ - \ {\color{Goldenrod}\sin}\ {\color{MidnightBlue}z_{1}}\ {\color{Goldenrod}\sin}\ {\color{MidnightBlue}z_{2}} \ \]



\[ {\color{Green}\tan}\ \left( {\color{MidnightBlue}z_{1}} + {\color{MidnightBlue}z_{2}} \right) \ = \ \frac{ {\color{Green}\tan}\ {\color{MidnightBlue}z_{1}} \ + \ {\color{Green}\tan}\ {\color{MidnightBlue}z_{2}}\ } { 1 - {\color{Green}\tan}\ {\color{MidnightBlue}z_{1}} \ {\color{Green}\tan}\ {\color{MidnightBlue}z_{2}}\ } \]


\[ {\color{Brown} \cot}\ \left( {\color{MidnightBlue}z_{1}} + {\color{MidnightBlue}z_{2}} \right) \ = \ \frac{ {\color{Brown} \cot}\ {\color{MidnightBlue}z_{1}} \ {\color{Brown} \cot}\ {\color{MidnightBlue}z_{2}}\ - 1 } { {\color{Brown} \cot}\ {\color{MidnightBlue}z_{1}} \ \ + \ {\color{Brown} \cot}\ {\color{MidnightBlue}z_{2}}\ } \]

Read 1984 times Last modified on Wednesday, 12 February 2014 16:45
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