Simplify 1-csc(x)^2

Problem

1−csc2(x)

Solution

1. Identify the relevant trigonometric identity involving the cosecant function.

2. Recall the Pythagorean identity relating cotangent and cosecant.

1+cot2(x)=csc2(x)

3. Rearrange the identity to match the form of the given expression by subtracting csc2(x) and cot2(x) from both sides.

1−csc2(x)=−cot2(x)

Final Answer

1−csc2(x)=−cot2(x)

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