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)`

#=((sinxcosy)/(cosxcosy)+(cosxsiny)/(cosxcosy))/((cosxcosy)/(cosxcosy)+(sinxsiny)/(cosxcosy)) -2tan(x+y)#

`=(tanx+tany)/(1+tanxtany)-(2(tanx+tany))/(1-tanxtany)`

`=(((tanx+tany)(1-tanxtany-2-2tanxtany))/(1-tan^2xtan^2y))`

`=((tanx+tany)(-1-3tanxtany))/(1-tan^2xtan^2y)`

`=((tanx+tany)(1+3tanxtany))/(tan^2xtan^2y-1)`