To simplify the expression, we'll start by converting all the trigonometric functions to their respective values using the unit circle.

cos 105° = cos (60° + 45°) = cos 60° cos 45° - sin 60° sin 45°
cos 105° = (1/2)(√3/2) - (√3/2)(√2/2) = √3/4 - √6/4 = (√3 - √6)/4

sin 15° = sin (60° - 45°) = sin 60° cos 45° - cos 60° sin 45°
sin 15° = (√3/2)(√2/2) - (1/2)(√2/2) = (√6 - √2)/4

cos 60° = 1/2

Now we substitute these values back into the expression:

(10cos105°/sin15°) cos60° = [(10 (√3 - √6)/4)/((√6 - √2)/4)] (1/2)
= 10(√3 - √6)/(√6 - √2) (1/2)
= 5(√3 - √6)/(√6 - √2)

Therefore, the simplified expression is 5(√3 - √6)/(√6 - √2).