Simplify (cot(x))/(tan(x))

Problem

cot(x)/tan(x)

Solution

1. Express in terms of sine and cosine using the quotient identities cot(x)=cos(x)/sin(x) and tan(x)=sin(x)/cos(x)

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

2. Multiply by the reciprocal of the denominator to simplify the complex fraction.

cos(x)/sin(x)⋅cos(x)/sin(x)

3. Multiply the numerators and denominators to combine the terms.

cos2(x)/sin2(x)

4. Apply the quotient identity cot(x)=cos(x)/sin(x) to rewrite the expression as a single trigonometric function.

(cos(x)/sin(x))2=cot2(x)

Final Answer

cot(x)/tan(x)=cot2(x)

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