Simplify cos(x)*csc(x)

Problem

cos(x)*csc(x)

Solution

1. Identify the trigonometric identity for the cosecant function.

csc(x)=1/sin(x)

2. Substitute the identity into the original expression.

cos(x)⋅1/sin(x)

3. Multiply the terms to form a single fraction.

cos(x)/sin(x)

4. Apply the cotangent identity, which states that the ratio of cosine to sine is cotangent.

cos(x)/sin(x)=cot(x)

Final Answer

cos(x)*csc(x)=cot(x)

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