Cot[Arctan(y)] = tan[Arccot(y)] = 1/y

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SUMMARY

The equation cot[Arctan(y)] = tan[Arccot(y)] = 1/y is established through the fundamental relationships between trigonometric functions. Specifically, cot(arctan(y)) simplifies to 1/tan(arctan(y)), which directly results in 1/y. This relationship holds true due to the definitions of cotangent and tangent in relation to their respective inverse functions, confirming the equality across both expressions.

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Alexx1
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Hello,

can someone prove this please?

cot[Arctan(y)] = tan[Arccot(y)] = 1/y
 
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cot(u) = 1/tan(u)

cot(arctan(y)) = 1/tan(arctan(y))

1/y

The other one's the same, with tan(u) = 1/cot(u) as the relationship.
 
Thx!
 

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