Simplify csc(63)^2-cot(63)^2

Problem

csc(63)−cot(63)

Solution

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

2. Recall the Pythagorean identity for these functions, which states that for any angle θ 1+cot(θ)=csc(θ)

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

csc(θ)−cot(θ)=1

4. Substitute the specific angle θ=63 into the rearranged identity.

csc(63)−cot(63)=1

Final Answer

csc(63)−cot(63)=1

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