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First, I assume the question refers to tan(90 degrees) not Ten90' because (apart from the incorrect spelling of tan) 90' represents 90 minutes or 90/60 degrees = 1.5 degrees.
The tangent of an angle is defined as the ratio of sine to cosine of the angle. When that angle is 90 degrees, the cosine is zero and so calculation of tan involves division by 0. And, in mathematics division by 0 is not infinity - it is not defined.
So, tan(90) is NOT infinity. It is not defined.
tan90 has a positive asymptote when you approach 90 degrees from below but has a negative asymptote when you approach from above.
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