proposition: Lemma cos_asin x : -1 <= x <= 1 -> cos (asin x) = Num.sqrt (1 - x^+2).
proof: Proof. move=> xB; rewrite -[LHS]ger0_norm; first by rewrite -sqrtr_sqr cos2sin2 asinK. by apply: cos_ge0_pihalf; rewrite asin_lepi2 // asin_geNpi2. Qed.
imports: mathcomp(all_ssreflect ssralg ssrint ssrnum matrix) mathcomp(interval rat) mathcomp(mathcomp_extra boolp classical_sets functions) reals ereal nsatz_realtype signed topology normedtype landau sequences derive realfun exp