Simplify 5sec(x)^2-10

Problem

5*sec2(x)−10

Solution

1. Factor out the greatest common factor, which is 5

5*(sec2(x)−2)

2. Apply the Pythagorean identity sec2(x)=1+tan2(x) to rewrite the expression in terms of the tangent function.

5*(1+tan2(x)−2)

3. Combine the constant terms inside the parentheses.

5*(tan2(x)−1)

Final Answer

5*sec2(x)−10=5*(tan2(x)−1)

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