Can someone please explain how to simplify this proiblem:

Question

cotx/sec^2 + cotx/csc^2

Answer 1

(cos/sin)/(1/ cos^2)+(cos/sin)/(1/sin^2)

cos^3/sin + cos sin

cos^3/sin + cos sin^2/sin

cos (cos^2 + sin^2)/sin
but cos^2 + sin^2 = 1
so
cos/sin
or
cot x

Answer 2

what happens to the cosine on the right side, when its in this step

cos^3x/sinx + cosxsinx^2/sinx