Simplify cot(arctan(x/( square root of 3)))

Problem

cot(arctan(x/√(,3)))

Solution

1. Identify the relationship between the trigonometric functions. The expression involves the cotangent of an inverse tangent, and we know the identity cot(θ)=1/tan(θ)

2. Let θ=arctan(x/√(,3)) By the definition of the inverse tangent function, this implies tan(θ)=x/√(,3)

3. Apply the reciprocal identity to the original expression. Since the expression is cot(θ) we substitute the reciprocal of the tangent.

4. Substitute the value of tan(θ) into the reciprocal formula:

cot(θ)=1/tan(θ)

5. Simplify the resulting fraction by taking the reciprocal of x/√(,3)

1/x/√(,3)=√(,3)/x

Final Answer

cot(arctan(x/√(,3)))=√(,3)/x

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