The more you understand, the less you have to memorize. A good
example is trigonometric identities, of which there are quite a
number. Should a student memorize trigonometric identities?
Well, at first, it is probably wise to memorize a few of them.
Part of a teacher’s job is to help students identify what is
essential to memorize, and what is more peripheral. In the case
of trig identities, the most important ones are Even the signs
are superfluous in equations (2) and (3); one can remember the
top signs only, and make use of the symmetry properties of the
sine and cosine functions (i.e, sine is odd and cosine is even).
That is, to derive the bottom signs from the top signs, just
replace by , and use the facts that and on the right sides of
equations (2) and (3). Now divide each term of equation (1) by
and you will get another standard identity; similarly if you
divide each term of equation (1) by . Let in equation (2) (with
the plus signs), and you will instantly derive another important
identity, . Similar