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Integrate[1/(a^2 - b^2*Cos[c*x]^2), x] ==
ArcTan[(a*Tan[c*x])/Sqrt[a^2 - b^2]]/ (a*Sqrt[a^2 - b^2]*c)

                  1
Integrate[-----------------, x] == 
           2    2         2
          a  - b  Cos[c x]

        a Tan[c x]
ArcTan[-------------]
             2    2
       Sqrt[a  - b ]
---------------------
          2    2
  a Sqrt[a  - b ] c