Simplify cot(arctan(x))

Problem

cot(arctan(x))

Solution

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

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

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

4. Substitute the value of tan(θ) back into the expression. Since tan(θ)=x then cot(θ)=1/x

Final Answer

cot(arctan(x))=1/x

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