Hi Lexie,
I am not quite sure what you mean by "two equations", where you only give x=cosx. In theory this can be plotted using:
Plot[{x, Cos[x]}, {x, -1, 3}]
There are various ways to solve this. For example:
FindRoot[x == Cos[x], {x, 1}]
(*{x -> 0.739085}*)
or
NSolve[{x == Cos[x] && x > 0 && x < Pi/2}, x]
(*{{x -> 0.739085}}*)
Cheers,
Marco