Simplify (cos(x))/(sin(x)cot(x))

Problem

cos(x)/(sin(x)*cot(x))

Solution

1. Identify the trigonometric identity for the cotangent function.

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

2. Substitute the identity into the denominator of the original expression.

cos(x)/(sin(x)⋅cos(x)/sin(x))

3. Simplify the denominator by canceling the sin(x) terms.

sin(x)⋅cos(x)/sin(x)=cos(x)

4. Divide the numerator by the simplified denominator.

cos(x)/cos(x)=1

Final Answer

cos(x)/(sin(x)*cot(x))=1

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