Simplify and express preferentially with sine : trigsin

trigsin takes as argument an expression containing trigonometric functions.
trigsin simplify this expression with the formula :
sin(x)2 + cos(x)2 = 1, tan(x) = $${\frac{{\sin(x)}}{{\cos(x)}}}$$ and tries to rewrite the expression only with sine.
Input :

trigsin(sin(x)^4+cos(x)^2+1)

Output :

sin(x)^4-sin(x)^2+2