They are different trigonometric ratios!
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It is 90 degrees between the circle's diameter and its tangent
The secant function is not defined for odd multipls of 90o.
The secant of an angle is the reciprocal of the cosine of the angle. So the secant is not defined whenever the cosine is zero That is, whenever the angle is a multiple of 180 degrees (or pi radians).
The secant of a circle passes through the center of a circle sometimes
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