Simplify sec(x)^3-sec(x)^2-sec(x)+1

Problem

sec(x)−sec(x)−sec(x)+1

Solution

1. Group terms to prepare for factoring by grouping.

sec(x)−sec(x)−sec(x)+1=(sec(x)−sec(x))−(sec(x)−1)

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

sec(x)*(sec(x)−1)−1*(sec(x)−1)

3. Factor out the common binomial (sec(x)−1)

(sec(x)−1)*(sec(x)−1)

4. Apply the Pythagorean identity tan(x)=sec(x)−1 to simplify the second factor.

(sec(x)−1)*tan(x)

Final Answer

sec(x)−sec(x)−sec(x)+1=(sec(x)−1)*tan(x)

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