(*********************************************************)
(** * Additional shift lemmas for sin, cos, tan          *)
(*********************************************************)

(* Specifications: *)
Lemma sin_pi_minus : forall x,
sin (PI - x) = sin x.
Lemma sin_pi_plus : forall x,
sin (PI + x) = - sin x.
Lemma cos_pi_minus : forall x,
cos (PI - x) = - cos x.
Lemma cos_pi_plus : forall x,
cos (PI + x) = - cos x.
Lemma tan_pi_minus : forall x, cos x <> 0 ->
tan (PI - x) = - tan x.
Lemma tan_pi_plus : forall x, cos x <> 0 ->
tan (PI + x) = tan x.