You should KNOW 

1. That the trig functions are intricately related by 
many identities i.e. formulas that are true for all 
values.  When indicated, these must be MEMORIZED with
understanding. Formulas will not be provided on exams.
(Note: But you don't need everything in the books--only the 
ones listed here.  In most cases these can be easily 
remembered and understood in graphical/geometric terms,
or can be easily deduced from others.)

2. The Pythagorean identity:  sin^2(x) + cos^2(x)=1, how it
is related to the Pythagorean Theorem, the 
identity  tan^2(x) + 1 =  sec^2(x) that can be derived
from it by  dividing everything by cos^2(x), and the similar
identity involving cot and csc.  NOTE: sin^2(x) is just a 
convenient way of writing  [sin(x)]^2 !  

3. The odd/even identities: cos(x)=cos(-x), sin(-x)=-sin(x), etc.,
which can be remembered either by recalling that the
sin function is odd and the cos function is even, by the 
appearance of the sin and cos graphs, or by the definitions
of sin and cos as coordinates of points on the unit circle and
the meaning of positive/negative angles.

4. The sum and difference identities for sin(x+y), cos(x+y).
These must simply be memorized, but these are the ONLY
identities that you really need to memorize.  You can get the 
others from these.  For example the identity for sin(x-y) can
be obtained from sin(x + (-y)) and the odd/even identities. 
You don't need to remember the tan(x+y) identity.

5. The double angle identities for sin(2x), cos(2x).  These can
be easily obtained from the sum identities since 
sin(2x) = sin(x + x), etc.  You don't need to remember the 
half-angle identities. 

6. The cofunction identities: e.g. sin(pi/2 - x) = cos x, 
cos(pi/2 -x) = sin x, etc.  These can be easily remembered by 
thinking of the complementary angles in a right triangle:
The sin of one is the cosine of the other.  

 7. The period identities:  sin(x + 2pi) = sin x, sin(x + pi) = -sin x.
(Think of the graphs of the sin and cos functions.)

You should be ABLE TO

1.  Use the basic identities together with your knowledge of
algebra to simplify trigonometric expressions. 

2. Make simple deductions of one identity from others, e.g.
deduce the identity for  sin(2x) from the sin(x+y) identity.

3.  Use trig identities to determine trig functions of angles 
from other trig functions of related angles, e.g.  Find 
tan x from knowledge of sin x,  find  sin(x+y) from knowledge
of sin x, sin y, cos x, cos y, etc.