Simplify sec(theta)^2-tan(theta)^2

Problem

sec2(θ)−tan2(θ)

Solution

1. Identify the fundamental Pythagorean identity relating the secant and tangent functions.

2. Recall the identity which states that one plus the square of the tangent of an angle is equal to the square of the secant of that angle.

1+tan2(θ)=sec2(θ)

3. Rearrange the identity by subtracting tan2(θ) from both sides of the equation to isolate the constant.

sec2(θ)−tan2(θ)=1

Final Answer

sec2(θ)−tan2(θ)=1

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