Solution:

Output due to input delayed by T seconds,

$y(t, T)=x(t-T) \sin w t$

Output delayed by T seconds,

$ \begin{gathered} y(t-T)=x(t-T) \sin w(t-T) \\\\ \because y(t, T) \neq y(t-T)\\ \end{gathered} \\ $

The given system is time-variant.