Simplify 1/(tan(x))

Problem

1/tan(x)

Solution

1. Identify the trigonometric identity for the tangent function in terms of sine and cosine.

tan(x)=sin(x)/cos(x)

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

1/tan(x)=1/sin(x)/cos(x)

3. Simplify the complex fraction by multiplying the numerator by the reciprocal of the denominator.

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

4. Recognize the resulting expression as the definition of the cotangent function.

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

Final Answer

1/tan(x)=cot(x)

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