Form :- ($\infty$/→$\infty$) => indeterminate form.
$\lim_{x→\infty}$ [sin(x) / x] = 0, because the value of sin(x) is between [-1,1]. Similarly, $\lim_{x→\infty}$ [cos(x) / x] = 0, because the value of cos(x) is also between [-1,1]. (finite number/$\infty$ = 0) (Think intuitively)
$\lim_{x→\infty}$ (x – sin(x)) / (x + cos(x))
= $\lim_{x→\infty}$ (1 – sin(x)/x) / (1 + cos(x)/x)
= $\lim_{x→\infty}$ (1 – 0) / (1 + 0)
= 1