Simplify (sec(x)^2-1)/(sec(x)-1)

Problem

(sec2(x)−1)/(sec(x)−1)

Solution

1. Identify the numerator as a difference of squares in the form a2−b2 where a=sec(x) and b=1

2. Factor the numerator using the identity a2−b2=(a−b)*(a+b)

sec2(x)−1=(sec(x)−1)*(sec(x)+1)

3. Substitute the factored expression back into the original fraction.

((sec(x)−1)*(sec(x)+1))/(sec(x)−1)

4. Cancel the common factor (sec(x)−1) from the numerator and the denominator.

sec(x)+1

Final Answer

(sec2(x)−1)/(sec(x)−1)=sec(x)+1

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