Solve the following differential equation: `tany(dy)/(dx)=sin(x+y)+sin(x-y)`

Explanation

`tany{dy} /{dx}=sin(x+y)+sin {x-y)`


`Rightarrow frac{d y}{d x}=frac{sin (x+y)+sin (x-y)}{tan y}`


`Rightarrow frac{d y}{d x}=frac{2 sin x cos y}{tan y}`


`Rightarrow frac{tan y}{cos y} d y=2 sin x d x`


`Rightarrow frac{sin y}{cos ^{2} y d y}=2 sin x d x`


Integrating both sides


`int frac{sin y}{cos ^{2} y d y}=int 2 sin x d x`


`1 / cos y=c-2 cos x`