Simplify cot(x)tan(x)

Problem

cot(x)*tan(x)

Solution

1. Identify the trigonometric identities for the cotangent and tangent functions in terms of sine and cosine.

2. Substitute the identities cot(x)=cos(x)/sin(x) and tan(x)=sin(x)/cos(x) into the expression.

cos(x)/sin(x)⋅sin(x)/cos(x)

3. Cancel the common terms in the numerator and the denominator.

cos(x)/cos(x)⋅sin(x)/sin(x)

4. Simplify the resulting product.

1⋅1=1

Final Answer

cot(x)*tan(x)=1

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