Factor csc(x)^3-csc(x)^2-csc(x)+1

Problem

csc(x)−csc(x)−csc(x)+1

Solution

1. Group the terms to prepare for factoring by grouping.

csc(x)−csc(x)−csc(x)+1=(csc(x)−csc(x))−(csc(x)−1)

2. Factor out the greatest common factor from each group.

csc(x)*(csc(x)−1)−1*(csc(x)−1)

3. Factor out the common binomial (csc(x)−1) from the expression.

(csc(x)−1)*(csc(x)−1)

4. Apply the difference of squares formula to the second factor, where a2−b2=(a−b)*(a+b)

(csc(x)−1)*(csc(x)−1)*(csc(x)+1)

5. Simplify the expression by combining the identical factors.

(csc(x)−1)2*(csc(x)+1)

Final Answer

csc(x)−csc(x)−csc(x)+1=(csc(x)−1)2*(csc(x)+1)

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