### 2.21.16 Rewrite sin, cos, tan in terms of tan(x/2) : `halftan`

`halftan` takes as argument an expression containing trigonometric functions.
`halftan` rewrites sin(x), cos(x) and tan(x) in terms of tan(x/2).
Input :

`halftan(sin(2*x)/(1+cos(2*x)))`

Output :

`2*tan(2*x/2)/((tan(2*x/2))```^```2+1)/`
`(1+(1-(tan(2*x/2))```^```2)/((tan(2*x/2))```^```2+1))`

Output, after simplification with `normal(ans())` :

`tan(x)`

Input :

`halftan(sin(x)```^```2+cos(x)```^```2)`

Output :

`(2*tan(x/2)/((tan(x/2))```^```2+1))```^```2+`
`((1-(tan(x/2))```^```2)/((tan(x/2))```^```2+1))```^```2`

Output, after simplification avec `normal(ans())` :

`1`