Question

How do you simplify `4cos(x+y)-8tan(x-y)` to trigonometric functions of x and y?

Answer 1

`4(cosxcosy-sinxsiny)-8((tanx-tany)/(1+tanxtany))`

Explanation:

To simplify`4cos(x+y)-8tan(x-y)`, we can use the following two identities

`cos(x+y)=cosxcosy-sinxsiny`

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

Hence `4cos(x+y)-8tan(x-y)`

= `4(cosxcosy-sinxsiny)-8((tanx-tany)/(1+tanxtany))`