Simplify sec(x)tan(x)^2+sec(x)

Problem

sec(x)*tan2(x)+sec(x)

Solution

1. Identify the common factor in both terms of the expression.

2. Factor out the common term sec(x) from the expression.

sec(x)*(tan2(x)+1)

3. Apply the Pythagorean identity which states that tan2(x)+1=sec2(x)

sec(x)*(sec2(x))

4. Multiply the terms to simplify the expression to a single trigonometric power.

sec3(x)

Final Answer

sec(x)*tan2(x)+sec(x)=sec3(x)

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