1 \(L_{A}\left [ -\sin t\right ] =\left ( D^{2}+1\right ) \left ( -\sin t\right ) =\left ( D\left ( D\left ( -\sin t\right ) \right ) -\sin t\right ) =\left ( D\left ( -\cos t\right ) -\sin t\right ) =\left ( \sin t-\sin t\right ) =0\)