Question

Simplify 1/(csc(x) - cot(x)) - 1/(csc(x) cot(x)).:

a) sin(x)
b) cos(x)
c) tan(x)
d) csc(x)

Answer 1

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.