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Essence
Memorizing
Basic
Formulas
Sum and Difference Formulas
Double & Triple Angle Formulas
Half Angle Formulas
Product to Sum Formulas
Sum to Product Formulas
All Formulas
Summarizing
Examples
Exercises
Final thoughts
Double-Angle Formulas:
In Sum and Difference formulas, if 
and 
are the same angle,
which we let them equal to 
, then you get these
Double Angle formulas. Also, a 2 always appears in the formulas, as
a coefficient 2 or as a square. The term 
is a term that shows up a lot (3 times). Being
strong in these formulas will make solving identities a lot easier.
The term 
is also common
in real problems.
Formula 1, the product of mixed functions sine and cosine, just don't forget the coefficient 2.
Formula 2, remember that on the
right side cosine and sine are all squared and it is the
square of cosine minus the square
of sine. Be aware of the order of
the subtraction. Try to compare with 
.
Formulas 3 and 4 come from formula 2
by using . Notice the order of the terms: equals to 
but not 
; 
but not 
. Later, in Understanding the Formulas we
will talk more about this.
Formula 5,
from the Sum formulasof tangent we can easily get this one
when angle = = .
There is also one more thing we want to mention, which is the Triple Angle formulas. They are not in most books, but we want to let you know them, because sometime you will need them to prove identities.
