For the first one, I'm not sure how you got 1 hehe

cos(x)sin(x) (sec(x)-csc(x))

(cos(x)sin(x)/cos(x)) - (cos(x)sin(x)/sin(x))

sin(x) - cos(x)

and for the fourth one..

Cot(x) (cot(x)+tan(x)) = csc^2(x)

multiply out..

cot^2(x) + (cot(x)tan(x)) = csc^2(x)

cot^2(x) + 1 = csc^2(x)

which is a common trig identity

and for the last one...

make a common denominator, and remember that sin^2(x) + cos^2(x) = 1. then just do some algebra magic