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(* Specifications: *)
Lemma tan_plus :
forall x y:R,
cos x <> 0 ->
cos y <> 0 ->
cos (x + y) <> 0 ->
1 - tan x * tan y <> 0 ->
tan (x + y) = (tan x + tan y) / (1 - tan x * tan y).
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Lemma exist_cos : forall x:R, { l:R | cos_in x l }.
Definition cos (x:R) : R := let (a,_) := exist_cos (Rsqr x) in a.
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Lemma exist_sin : forall x:R, { l:R | sin_in x l }.
Lemma sin_antisym : forall x:R, sin (- x) = - sin x.
Lemma sin_0 : sin 0 = 0.
(* Value of [cos 0] *)
Lemma cos_0 : cos 0 = 1.