Question

cos(x)/(1-tan(x)) + (sin (x))* cos(x))/ sin (x)-cos(x))

Answer 1

In the second term, I counted 6 of "(" and 7 of ")",

so mismatched brackets.
I will assume you meant:
cos(x)/(1-tan(x)) + (sin (x))* cos(x))/ (sin (x)-
cos(x))
then:
= cosx/( 1 - sinx/cosx) + sinx cosx/(sinx - cosx)
= cosx/( (cosx - sinx)/cosx) - sinxcosx/(cosx-sinx)
= cos^2 x/(cosx - sinx) - sinxcosx/(cosx-sinx)
= (cos^2 x - sinxcosx)/(cosx - sinx)
= cosx(cosx - sinx)/(cosx - sinx)
= cosx , if sinx ≠ cosx