Simplify csc(x)^2

Problem

csc2(x)

Solution

1. Identify the expression as the square of the cosecant function.

2. Apply the reciprocal identity for the cosecant function, which states that csc(x)=1/sin(x)

3. Square the identity to express the original term in terms of the sine function.

4. Apply the Pythagorean identity if an alternative form is needed, where sin2(x)+cos2(x)=1 or use the identity 1+cot2(x)=csc2(x)

Final Answer

csc2(x)=1+cot2(x)

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