[Index]
- Introduction
- Essence
- Memorizing
- Understanding
- Summarizing
- Examples
- Exercises
- Final thoughts
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Sum and Difference Formulas:
There are four possible products of
two factors that can be formed from 
, 
, 
, and 
. Namely: 
, 
, 
, 
. Note their
distribution in the first four formulas. The right hand sides of
(1) and (2) consist of the algebraic sum of and , while (3) and (4)
consist of the mixed products. Note the distribution of signs
below.
In formulas 1 and 2, for cosine the signs on each side of the formulas are "opposite". Be aware of the order of the subtraction: the product of cosine minus the product of sine.
In formulas 3 and 4, for sine the signs on both sides are the
same. Be aware of the subtraction in formula 4: in front of the
product is negative, when the product contains the factor , where 
is from the term of
.
Formulas 5 and 6, tangents have the same sign in the numerator
of both sides. The numerator is also what you get if you multiply
tangent by 
(i.e. 
. Notice, this is
not actually how it works). The denominator is 
, the sign being the opposite of the
numerator.
