Solution
= Solution
For each fixed $x$, $x/n\to0$, so the <pointwise limit> is $1$. Moreover $1-\cos u=2\sin^2(u/2)\le u^2/2$ gives
$$
\sup_{0<x<1}|\cos(x/n)-1|\le\frac1{2n^2}\longrightarrow0.
$$
Thus \b[the limit is $1$, with <uniform convergence> on $(0,1)$].