This trigonometric ratio states the ratio between the adjacent side to a certain angle and the opposite side to the angle. It gives no indication about the lengths of the sides.
When the adjacent side and the opposite side lengths for a given angle change, if their ratio stays the same, then the cotangent, too, would stay the same. In addition, note that the cotangent of θ is also the reciprocal of the tangent of θ.
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