Simplify (cos(x)^2)/(cot(x)^2)

Problem

cos2(x)/cot2(x)

Solution

1. Identify the trigonometric identity for the cotangent function.

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

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

cos2(x)/((cos(x)/sin(x))2)

3. Apply the power to the fraction in the denominator.

cos2(x)/cos2(x)/sin2(x)

4. Multiply the numerator by the reciprocal of the denominator.

cos2(x)⋅sin2(x)/cos2(x)

5. Cancel the common factor of cos2(x) from the numerator and the denominator.

sin2(x)

Final Answer

cos2(x)/cot2(x)=sin2(x)

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