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## 2. What is the essence of verifying an identity?The purpose of verifying an identity
is to prove that the two sides of the equation are equal. If the
two sides are the same, we need to verify nothing. When an identity
needs to be proved, the two sides of the equal sign have to be
formally different. The first and most essential thing to do in
this situation is to identify the differences between the two
sides. It is guaranteed in here that there are only three differences
or less between the two sides: Verify the followings: In example 1, there are no differences of functions or operations
because both sides have In example 2, first of all we see the difference of functions.
The left side has In example 3, there are all kinds of differences. There is difference
of functions since the left side has In example 4, again we have all kinds of differences. Differences
of functions: From the four examples above, we had an identity with one difference,
one with two differences, and two with three differences. There
is never going to be an identity with more than three differences,
at least not that we know of, and it is very important to keep
that in mind. We like to say that We know that |
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