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

Problem

tan2(θ)−sec2(θ)

Solution

1. Identify the relevant trigonometric identity relating the tangent and secant functions.

2. Recall the Pythagorean identity for tangent and secant.

tan2(θ)+1=sec2(θ)

3. Rearrange the identity to match the form of the given expression by subtracting sec2(θ) and 1 from both sides.

tan2(θ)−sec2(θ)=−1

Final Answer

tan2(θ)−sec2(θ)=−1

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