intro; rewrite <- Rsqr_mult; rewrite DRs; rewrite Rs_alphas;
repeat rewrite Rsqr_mult; rewrite Rplus_comm;
rewrite <- (Rmult_comm (Rsqr (cos (thetat t - alphas t))));
rewrite <- (Rmult_comm (Rsqr (sin (thetat t - alphas t))));
rewrite <- Rmult_plus_distr_r; rewrite sin2_cos2;
rewrite Rmult_1_l; reflexivity.
Qed.

(**********)
Lemma Rs_pos : forall t : R, (0 <= Rs t)%R.
intro; unfold Rs in |- *; apply sqrt_positivity; apply Rplus_le_le_0_compat;
apply Rle_0_sqr.