Question

Verify each identity:
(tanx+tany)/(1-tanxtany)=(sinxcosy+cosxsiny)/(cosxcosy-sinxsiny)

Answer 1

\[tanx=\frac{sinx}{cosx}\]\[tany=\frac{siny}{cosy}\]
\[\large{\frac{tanx+tany}{1-tanxtany}=\frac{(\frac{sinx}{cosx})+(\frac{siny}{cosy})}{1-\frac{sinx}{cosx}\frac{siny}{cosy}}}\]now multiply top and bottom by cosxcosy
\[\large{=\frac{(\frac{sinx}{\cancel{cosx}})\times \cancel{cosx} cosy +(\frac{siny}{\cancel{cosy}}\times cosx \cancel{cosy})}{(1 \times cosxcosy)-(\frac{sinxsiny}{\cancel{cosxcosy}} \times \cancel{cosxcosy})}}\]

Answer 2

thank you! @lalaly :)

Answer 3

your welcome:D

Answer 4

@alessandro96