Question

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

Answer 1

`tan(x+y)-cos(x-y)=(tanx+tany)/(1-tanxtany)+cosxcosy+sinxsiny`

Explanation:

We know that `tan(A+B)=(tanA+tanB)/(1-tanAtanB)` and `cos(A-B)=cosAcosB+sinAsinB`

Using these identities, we get

`tan(x+y)-cos(x-y)`

= `(tanx+tany)/(1-tanxtany)+cosxcosy+sinxsiny`,

which are trigonometric functions of `x` and `y`