Verify the identity cscx+cotx=sinx/(1-cosx).

We'lll manage only the left side and we'll re-write the
terms of the sum:

csc x = 1/sin x and cot x = cos x/sin
x

csc x + cot x = 1/sin x + cos x/sin
x

Since the fractions have the same denominator, we can
write:

csc x + cot x = (1+cos x)/sin
x

The expression will
become:

(1+cos x)/sin x = sin x/(1 - cos
x)

We'll cross multiply:

(sin
x)^2 = (1+cos x)(1-cos x)

The product from the right side
returns the difference of two squares:

(sin x)^2 = 1 - (cos
x)^2

We'll add (cos x)^2 both
sides:

(sin x)^2 + (cos x)^2 =
1

But Pythagorean identity states that (sin x)^2 + (cos
x)^2 = 1, therefore we've came up with a true
statement.

Therefore, the given identity csc
x + cot x = sin x/(1 - cos x) is verified.