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A calculation is a tautology. In mathematics, this means that at the left and right of the equal sign (=) the same is stated.


Example 1

Some simple calculations show

If left and right are not identical you have made a mistake. That is it.


Example 2

You can solve the equation

x2 = 2x

as for x = 2 it gives

22 = 22     ⇒     4 = 4

and that is correct. You can easily see that. But there are more solutions. By trial and error you can find them.


Example 3

Substituting the definitions of the sine and the cosine in Euler's formula gives


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