Simplify sec(theta)^2

Problem

sec^2(θ)

Solution

1. Identify the expression as the square of the secant function, which is a fundamental trigonometric function.

2. Recall the Pythagorean identity that relates the secant function to the tangent function.

3. Apply the identity sec^2(θ)=1+tan^2(θ) to express the term in an alternative simplified form.

4. Note that sec^2(θ) is also the reciprocal of the cosine squared, which can be written as 1/cos^2(θ)

Final Answer

sec^2(θ)=1+tan^2(θ)

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