Evaluate
Cot (tan (2x) + Cot (2x)
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This function has no specific value. It cannot be easily simplified. Let’s say the question was written with an angle value like A instead of x. Because we’re going to reuse X, and Y. tan(A) = Y/X, where Y is the opposite side of a triangle, and X is the adjacent side. Then cot(A) = X/Y = 1/tan(A).
So tan^2(A) + cot^2(A) = (Y/X)^2 + (X/Y)^2 = (X^4 + Y^4) / (XY)^2.
Notice that when X = Y at 45 deg, this function becomes 2. But it starts at infinity at A=0 and goes back up to infinity at A=90 deg. It then repeats the same behavior over the next 90 deg., and twice more the same pattern to get back from 180 deg through 270 deg to 0 deg.
So there is no one value. It’s simply a function that ranges from 2 to infinity.
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