Simplify csc x - cos x cot x.?

Answer 1

1/sin(x) - cos(x) * cos(x)/sin(x)
1/sin(x) - cos^2(x)/sin(x)
(1-cos^2(x))/sin(x)
sin^2(x)/sin(x)
sin(x)

Answer 2

csc x = 1/sin x, cot x = cos x/sin x, Substituting these two:
1/sin x - cos^2 x/sin x =
(1-cos^2 x)/sin x = Now using the identity sin^2 x + cos^2 x = 1
sin^2 x/sin x =
sin x <- The answer.