Answer
$$=0.08$$
Work Step by Step
$$f_x= \cos y \\ f_x(0,0)=\cos 0=1 \\ f_y(x,y) =1-x \sin y \\ f_{y}(0,0) =1-0 \sin (0)=1 \\f_{xx}(x,y)=0 \\ f_{yy}(x,y)=-x \ cos y \\ f_{xy}(x,y) =- \sin y$$
Error; $|E(x,y)| \leq \dfrac{1}{2} \times 1 [ |x-0| +|y-0|)^2$
or, $$E \leq \dfrac{1}{2} \times (0.2+0.2)^2 =0.08$$
