Write the trigonometric expression in terms of sine and cosine, and then simplify.

cot(x)/csc(x)-sin(x)

Is this what you have?

ctn(x)/(csc(x)-sin(x)) ?

To write the trigonometric expression in terms of sine and cosine, we will express cot(x) and csc(x) using sine and cosine.

Recall that cot(x) is equal to cosine(x) divided by sine(x), and csc(x) is equal to 1 divided by sine(x).

So, cot(x)/csc(x) can be written as (cos(x)/sin(x)) / (1/sin(x)).

Now, let's simplify this expression:

(cos(x)/sin(x)) / (1/sin(x))

To divide two fractions, we multiply the first fraction by the reciprocal of the second fraction. Therefore, we have:

(cos(x)/sin(x)) * (sin(x)/1)

This simplifies to:

cos(x)

Finally, we subtract sin(x) from cos(x):

cos(x) - sin(x)

Therefore, the trigonometric expression cot(x)/csc(x)-sin(x) simplifies to cos(x) - sin(x).