(1)  Write several starting terms of the first series

         cos(x) = 1 -  +  -  .


     Replace here x with , since you want  .  You will get

          = 1 -  +  - .           (1)


     You should keep as many terms of this series to have at least the term with .



(2)  Write several starting terms of the second series

          =  -  +  .


     Replace here x with , since you want  .  You will get

          =  -  + .          (2)


     You should keep as many terms of this series to have at least the term with .



(3)  Using (1) and (2), form    +  - .   You will get

          +  -  =  1 -  +  -  

                                             +   -  +  - 1 =

         = some terms will cancel; other will remain; I will keep the remaining terms with .  It gives 

         = .   The other terms have x in degrees HIGHER than 12.



(4)  After dividing by ,  I have  plus other terms with x of degree higher than 1.

     When calculating the limit at x--> 0, these terms produce 0 (zero), so they are not interesting to me.



(5)  Thus I get the ANSWER:  the sough limit at  x --> 0  equals  .