### 2.21.22 Simplify and express preferentially with tangents : `trigtan`

`trigtan` takes as argument an expression
containing trigonometric functions.

`trigtan` simplifies this expression with the formula :

sin(*x*)2+cos(*x*)2=1, tan(*x*)=sin(*x*)/cos(*x*) and
tries to rewrite the expression only with tangents.

Input :

`trigtan(sin(x)``^`

`4+cos(x)``^`

`2+1)`

Output :

`((tan(x))``^`

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

`2))``^`

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

`2)+1`

Output, after simplification with `normal` :

`(2*tan(x)``^`

`4+3*tan(x)``^`

`2+2)/(tan(x)``^`

`4+2*tan(x))``^`

`2+1)`