To simplify the expression ((1-cos 2x)*cos x)/sin x, we can first expand the numerator using the double angle identity cos 2x = 2cos^2 x - 1:

((1 - (2cos^2 x - 1))cos x) / sin x
= ((1 - 2cos^2 x + 1)cos x) / sin x
= (2 - 2cos^2 x)*cos x / sin x
= 2cos x - 2cos^3 x / sin x

Next, we can use the trigonometric identity cos^2 x = 1 - sin^2 x to simplify the expression:

= 2cos x - 2(1 - sin^2 x)cos x / sin x
= 2cos x - 2cos x + 2sin^2 x / sin x
= 2sin x

Therefore, ((1-cos 2x)*cos x) / sin x simplifies to 2sin x.