Question

[sinxcosx/(1+cosx(]-[sinx/(1-cosx)]= -(cotxcosx+cscx)

Answer 1

multiply top and bottom of the left most by
(1-cos x)
multiply top and bottom of the second term on the left by (1 + cos x)
that gives you the common denominator on the left of (1 - cos^2 x) which is sin^2 x

then do the two multiplications on the top to get on the top
sin x cos x - sin x cos^2 x
and
- (sin x + cos x sin x)
combine for a numerator of
sin x cos x- sin x cos^2 x - sin x - sin x cos x
simplify and divide top and bottom by sin x
[- cos^2 x - 1]/sin x on the left

now work on the right
cot x = cos x/ sin x
so
- (cos^2 x / sin x + 1/sin x)
which is what you have on the left