**Note**: This questions is quite different from the ones referred to in the comments. Those deal with numerical questions, while this one is algebraic.

I have plots of the following type:

    Plot[Cos[50 t] + Cos[51 t], {t, 0, 10}]

![enter image description here][1]

I would like to plot a 'sheath' over this plot, i.e. another plot that joins all of maxima and minima of this plot respectively. Here is my attempt, but it's not exactly what I'd like:

    Plot[{Cos[50 t] + Cos[51 t], Cos[t] + 1.5, -Cos[t] - 1.5}, {t, 0, 10}]

  ![enter image description here][2]

How can I generate the actual, tight sheath?


  [1]: https://i.sstatic.net/LyJHJ.png
  [2]: https://i.sstatic.net/XFAQj.png