If the function
\[
f(x)=
\begin{cases}
\frac{\sin x}{x}+\cos x, & x\neq0\\
k, & x=0
\end{cases}
\]
is continuous at \(x=0\), then find the value of \(k\).
Show Hint
When computing limits containing basic trigonometric expressions at $0$, look for standard identities like \(\lim_{x \to 0} \frac{\sin x}{x} = 1\) or \(\lim_{x \to 0} \frac{\tan x}{x} = 1\) to simplify the expression immediately.