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(** * Express trigonometric functions with each other    *)
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(** ** Express sin and cos with each other *)

(* Specifications: *)
Lemma cos_sin : forall x, cos x >=0 ->
cos x = sqrt(1 - (sin x)²).
Lemma cos_sin_opp : forall x, cos x <=0 ->
cos x = - sqrt(1 - (sin x)²).
Lemma cos_sin_Rabs : forall x,
Rabs (cos x) = sqrt(1 - (sin x)²).
Lemma sin_cos : forall x, sin x >=0 ->
sin x = sqrt(1 - (cos x)²).
Lemma sin_cos_opp : forall x, sin x <=0 ->
sin x = - sqrt(1 - (cos x)²).
Lemma sin_cos_Rabs : forall x,
Rabs (sin x) = sqrt(1 - (cos x)²).