Let $f(x)=\sum\limits_{r=0}^{n} {(r+2)x^{2r}}$ and $g(x)=ax^2+\cos^2b+\sin b$ where $n\in\mathbb{N}$; $a,b\in\mathbb{R}$. If $d(n,a,b)$ represents shortest distance between curves $y=f(x)$ and $y=g(x)$ for given values of $n,a,b$; then
$\hbox{(A)}\quad d(2019,2020,b)=\frac34\,\forall b\in\mathbb{R}$
$\hbox{(B)}\quad d(n,-2018,b)=\frac34\,\forall b\in\mathbb{R},\, n\in\mathbb{N}$
$\hbox{(C)}\quad d(n,a,b)=\frac34\,\forall n\in\mathbb{N},\, a,b\in\mathbb{R}$
$\hbox{(D)}\quad d(2020,a,b)=\frac34\,\forall a,b\in\mathbb{R}$
I have tried simplyfying the two curves but nothing seems to be eminent wrt to the options given. Pls help.