Simplify and express preferentially with tangents : trigtan

### 5.21.23 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)