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

Problem

cos2(x)+cos2(x)*cot2(x)

Solution

1. Factor out the common term cos2(x) from the expression.

cos2(x)*(1+cot2(x))

2. Identify the Pythagorean identity for the term inside the parentheses.

1+cot2(x)=csc2(x)

3. Substitute the identity back into the expression.

cos2(x)*csc2(x)

4. Rewrite the cosecant function in terms of sine using the reciprocal identity csc(x)=1/sin(x)

cos2(x)⋅1/sin2(x)

5. Simplify the resulting fraction using the definition of the cotangent function cot(x)=cos(x)/sin(x)

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

Final Answer

cos2(x)+cos2(x)*cot2(x)=cot2(x)

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