Simplify (sin(x)csc(x))/(cot(x))

Problem

(sin(x)*csc(x))/cot(x)

Solution

1. Identify the reciprocal identity for the cosecant function, which is csc(x)=1/sin(x)

2. Substitute this identity into the numerator of the expression.

(sin(x)⋅1/sin(x))/cot(x)

3. Simplify the numerator by canceling the sin(x) terms, which results in 1

1/cot(x)

4. Apply the reciprocal identity for the cotangent function, where 1/cot(x)=tan(x)

tan(x)

Final Answer

(sin(x)*csc(x))/cot(x)=tan(x)

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