proposition: Theorem FFT : forall x : IR, Cos x[^]2[+]Sin x[^]2 [=] [1].
proof: Proof. intros. astepl (Cos x[*]Cos x[+]Sin x[*]Sin x). astepr (Cos [0]). apply eq_transitive_unfolded with (Cos (x[+][--]x)). 2: algebra. apply eq_symmetric_unfolded. eapply eq_transitive_unfolded. apply Cos_plus. unfold cg_minus in |- *. apply bin_op_wd_unfolded. algebra. astepl (Sin x[*][--] (Sin [--]x)). Step_final (Sin x[*][--][--] (Sin x)). Qed.
imports: CoRN.transc.Trigonometric