Here are the identities I've already mentioned:
 
tan( theta ) = [ sin( theta ) / cos( theta ) ]   cot( theta ) = [ cos( theta ) / sin( theta ) ]

sec( theta ) = [ 1 / cos( theta ) ]
 
csc( theta ) = [ 1 / sin( theta ) ]


tan^2( theta ) + 1 = cos^2( theta )


1 + cot^2( theta ) = csc^2( theta )


tan^2( theta ) + 1 = cos^2( theta )

Here are the others that come up a lot:


sin( 2 * theta ) = 2sin( theta ) * cos( theta )


cos( 2 * theta ) = cos^2( theta ) - sin^2( theta )  ... = 2cos^2( theta ) - 1  ...  = 1 - 2sin^2( theta )
Notice that these go in alphabetical order!
Also, the cosine guys are in the first position on both
and the sine guys are in the second position on both.