In mathematics, "tan" refers to the tangent function, which calculates the ratio of the opposite side to the adjacent side in a right triangle for a given angle. On the other hand, "tan⁻¹" (or arctan) is the inverse tangent function, which takes a ratio and returns the angle whose tangent is that ratio. Essentially, while tan gives you the tangent of an angle, tan⁻¹ helps you find the angle when you know the tangent value.
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It isn't, but here is a corrected equation that is: tan1 x tan 20 x tan 45 x tan 70 x tan 89 = 1 It will then work because tan(45 + x) = 1/tan(45 - x). Hence tan1 cancels when multiplied with tan89, and tan20 cancels with tan70. tan 45 equals 1, and so the whole expression cancels to 1. I think this effect was what the equation was intended to demonstrate.
There is no difference in meaning between the two. It is usually spelled in lowercase, though (arc tan, or arctan).
Sin = Opposite/Hypotenuse, tan = Opposite/Adjacent
a function key a scientific calculator called TAN
Usually there isn't any one website for math answers. So you should probably google whatever math question you have. For example, if you're working with sin, cos and tan, then you should look up "sin calculator", "cos calculator" or "tan calculator" or a variant depending on what you need help with, like "explanation of tan".