Verify the Identity tan(x)=1/(cot(x))

Problem

tan(x)=1/cot(x)

Solution

1. Identify the definition of the cotangent function in terms of the sine and cosine functions.

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

2. Substitute this definition into the denominator of the right side of the identity.

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

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

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

4. Recognize that the resulting ratio of sine to cosine is the definition of the tangent function.

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

Final Answer

tan(x)=1/cot(x)

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