Write an equation to represent a number increase by 4 is 7.
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This is not an identity but an equation. You're supposed to find the values of for which this is true. It is *not* true for all values of
.
To see why:
has period
, which means
.
The angle sum identity for says that
So
By definition of ,
and so
which is only 0 if either (which only happens for certain values of
) or
(which also only happens for certain values of
). It's these values of
you want to find.
whenever
is a multiple of
, i.e.
for any integer
.
If , then
is true for
and
. Then to account for all other possible values, we add a multiple of
, so that
or
for integers
.