Simplify cot(arctan(u))

Problem

cot(arctan(u))

Solution

1. Identify the relationship between the trigonometric functions. The expression involves the cotangent of an angle whose tangent is u

2. Define the angle θ such that θ=arctan(u) By the definition of the inverse tangent function, this implies tan(θ)=u

3. Apply the identity for the cotangent function. Recall that cot(θ)=1/tan(θ)

4. Substitute the value of tan(θ) into the identity. Since tan(θ)=u it follows that cot(θ)=1/u

Final Answer

cot(arctan(u))=1/u

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