sin(x)cos(x)=sin(2x)/2; cos2(x)-sin2(x)=cos(2x) are standard identities.
So on the left side we therefore have sin(2x)/2cos(2x)=tan(2x)/2 by definition of tangent.
tan(a+b)=(tan(a)+tan(b))/(1-tan(a)tan(b)) is another standard identity. When a=b=x:
tan(2x)=2tan(x)/(1-tan2(x)), and we have tan(2x)/2=tan(x)/(1-tan2(x)), which is the right side.
Therefore: sin(x)cos(x)/(cos2(x)-sin2(x))=tan(x)/(1-tan2(x)) QED