aa  =  Cos[1.4]

f[x_]  =  Log[Cos[x]]

D[f[x], x]

Exp[f[x]]

p  =  f[1.4]

Series[f[x], {x, 0, 30}]

p = N[1, 3000];   g[x_]  := Cos[x];
For[i = 1,  
      i ≤ 
        40,  i++,  
{p = 
          g[p],  
Print[i],  
        Print[N[p, 
            20]],   Print[ ],  
}
]

p = N[1, 3000];   g[x_]  := Cos[x] - x;
For[i = 1,  
      i ≤ 
        8,  i++,  
{p = 
          p  -  g[p]/g'[p],  
Print[i],  
        Print[N[p, 
            70]],   Print[ ],  
}
]