Question

How do you simplify `sin(x+y)/cos(x-y)-2tan(x-y)` to trigonometric functions of x and y?

Answer 1

`sin(x+y)/cos(x-y)-2tan(x-y)`

`=sin(x+y)/cos(x-y)-(2sin(x-y))/cos(x-y)`

`=(sinxcosy+cosxsiny-2sinxcosy+2cosxsiny)/cos(x-y)`

`=(3cosxsiny-sinxcosy)/(cosxcosy+sinxsiny)`

`=((3cosxsiny)/(cosxcosy) -(sinxcosy)/ (cosxcosy) )/((cosxcosy)/ (cosxcosy )+(sinxsiny) /( cosxcosy)`

`=(3tany-tanx)/(1+tanxtany)`