$($B points$)$ By using the linear approximation of the function $f(x,y)=1-$xycos$(y)$ at $(1,1),$ find the approximate value of $f(1\mathrm{.}02,0\mathrm{.}97).$

a$)2\mathrm{.}03$

b$)1\mathrm{.}99$

c$)2\mathrm{.}01$

d$)1\mathrm{.}98$

e$)2\mathrm{.}05$