Simplify (cos(x)sec(x))/(cot(x))

Problem

(cos(x)*sec(x))/cot(x)

Solution

1. Identify the reciprocal identity for the secant function, which is sec(x)=1/cos(x)

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

(cos(x)⋅1/cos(x))/cot(x)

3. Simplify the numerator by canceling the cos(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

(cos(x)*sec(x))/cot(x)=tan(x)

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