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Least value of tan2?T + cot2?T is

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Since these trigonometric functions are reciprocals of each other, when one is zero the other is at infinity. Therefore the lowest value for the sum of the squares of each the tangent and cotangent function would be where the value of each is 1 or -1 (at pi/4, 3pi/4, 5pi/4, 7pi/4). Therefore, the lowest value would be 2.