Expand the Trigonometric Expression sec(x)^2

Problem

sec2(x)

Solution

1. Identify the trigonometric identity relating the secant function to the tangent function.

2. Apply the identity sec2(x)=1+tan2(x) which is derived from the Pythagorean identity sin2(x)+cos2(x)=1 by dividing all terms by cos2(x)

3. Substitute the identity into the expression to represent it in an expanded form involving the tangent function.

Final Answer

sec2(x)=1+tan2(x)

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