Another form would be:
#[a] & /@ {Cos, Sin}
(* {Cos[a], Sin[a]} *)
What you're looking for is probably the following:
Through[{Cos, Sin}[a]]
(* {Cos[a], Sin[a]} *)
You can accomplish the above, by the way, with AngleVector[a].
Note that there are some other shorthand forms for these kind of things, at least MinMax, ReIm and AbsArg.
