Question

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

Answer 1

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

`=(sin x*cos y-cos x*sin y)/(cos x*cos y-sin x*siny)+(tan x - tan y)/(1+tan x*tan y)`

Explanation:

Use trigonometric identities for `sin`, `cos` and `tan` of sum and difference of angles:
`sin(x-y)=sin x*cos y - cos x*sin y`
`cos(x+y)=cos x*cos y - sin x*sin y`
`tan(x-y)=(tan x - tan y)/(1+tan x*tan y)`