Rewrite trigonometric functions as function of tan(x/2) and hyperbolic functions as function of exp(x):
halftan_hyp2exp

halftan_hyp2exp takes as argument a trigonometric and hyperbolic expression.
halftan_hyp2exp rewrites sin(x), cos(x), tan(x) in terms of tan(${\frac{{x}}{{2}}}$) and sinh(x), cosh(x), tanh(x) in terms of exp(x).
Input :

halftan_hyp2exp(tan(x)+tanh(x))

Output :

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

Input :

halftan_hyp2exp(sin(x)^2+cos(x)^2-sinh(x)^2+cosh(x)^2)

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

2