Convolution of h(n) & x(n)
HINT:

I assume that $n$ is an integer and that we're talking about discrete-time signals. You need to simplify the expressions for $h(n)$ by noting that $\delta(n)=1$ for $n=0$ and zero otherwise. So, for which values of $n$ does $\sin(1+|n|)$ equal zero, and for which values of $n$ does $\sin(2\pi n/N)$ equal zero?