Simplify (cot(a))/(tan(a))

Problem

cot(a)/tan(a)

Solution

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

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

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

cos(a)/sin(a)⋅cos(a)/sin(a)

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

cos2(a)/sin2(a)

4. Apply the cotangent identity cot(a)=cos(a)/sin(a) to write the expression in its simplest form.

cot2(a)

Final Answer

cot(a)/tan(a)=cot2(a)

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