Correct choice is (a) sin y (cos y-cos x)
For explanation: Δ=\begin{vmatrix}sin \,y&0&sin \,y\\cos \,y&1&cos \,x\\sin \,y&1&sin \,y \end{vmatrix}
Δ=sin y \begin{vmatrix}1&cos \,x\\1&sin \,y \end{vmatrix}-0\begin{vmatrix}cos \,y&cos \,x \\sin \,y&sin \,y \end{vmatrix}+sin y \begin{vmatrix}cos \,y&1\\sin \,y&1\end{vmatrix}
Δ=sin y (sin y-cos x)-0+sin y (cos y-sin y)
Δ=sin^2y-sin y cos x+sin y cos y-sin^2y=sin y (cos y-cos x)