Simplify csc(theta)^2-cot(theta)^2

Problem

csc2(θ)−cot2(θ)

Solution

1. Identify the trigonometric identity relating the cosecant and cotangent functions.

2. Recall the Pythagorean identity for these functions:

cot2(θ)+1=csc2(θ)

3. Rearrange the identity to match the given expression by subtracting cot2(θ) from both sides of the equation:

csc2(θ)−cot2(θ)=1

Final Answer

csc2(θ)−cot2(θ)=1

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