proposition: Lemma cos_2a_cos : forall x:R, cos (2 * x) = 2 * cos x * cos x - 1.
proof: Proof. intro x; rewrite <-Rplus_diag; unfold Rminus in |- *; rewrite Rmult_assoc; rewrite cos_plus; generalize (sin2_cos2 x); rewrite <-Rplus_diag; intro H1; rewrite <- H1; ring_Rsqr. Qed.
imports: Rbase Rfunctions SeqSeries Rtrigo_fun Rtrigo_def Rtrigo_alt Cos_rel Cos_plus ZArith_base Zcomplements Lia Lra Ranalysis1 Rsqrt_def PSeries_reg