Final answer:
To simplify the expression 1/(csc(x) - cot(x)) - 1/(csc(x) cot(x)), we multiply both fractions by the appropriate terms to find a common denominator. The simplified expression is cos(x) - 1.
Step-by-step explanation:
To simplify the expression 1/(csc(x) - cot(x)) - 1/(csc(x) cot(x)), we can start by finding the common denominator for the two fractions. The common denominator is csc(x) cot(x).
Next, we can multiply the first fraction by (cot(x))/(cot(x)) and the second fraction by (csc(x))/(csc(x)) to simplify.
After simplifying, we get (cot(x))/(csc(x)) - 1 = cos(x) - 1.
Therefore, the simplified expression is cos(x) - 1.