To simplify this expression, we can use the trigonometric identity:

sin (A - B) = sin A cos B - cos A sin B

Therefore, we can rewrite the expression as:

sin 59 cos 61 - sin 61 cos 59 / cos 58 cos 62 - sin 62 sin 58
= sin (59-61) / cos (58-62)
= sin (-2) / cos (-4)
= -sin 2 / cos 4

We know that sin 2 = sin 78 and cos 4 = cos 86, so:

-sin 2 / cos 4 = -sin 78 / cos 86

Therefore, the simplified expression is -sin 78 / cos 86.