Verify the Identity cot(x)=cos(x)csc(x)

Problem

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

Solution

1. Identify the right side of the identity to manipulate, which is cos(x)*csc(x)

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

3. Substitute the reciprocal identity into the expression:

cos(x)*csc(x)=cos(x)⋅1/sin(x)

4. Multiply the terms to combine them into a single fraction:

cos(x)⋅1/sin(x)=cos(x)/sin(x)

5. Apply the quotient identity for the cotangent function, where cot(x)=cos(x)/sin(x)

6. Conclude that the right side simplifies to the left side:

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

Final Answer

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

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