Answer
Conservative
Work Step by Step
When $F(x,y)=Ai+Bj$ is a conservative field, then throughout the domain $D$, we get
$\dfrac{\partial A}{\partial y}=\dfrac{\partial B}{\partial x}$
$a$ and $b$ are the first-order partial derivatives on the domain $D$.
We are given that $F(x,y)=\sin y i+(1+x \cos y) j$
Here, we have $\dfrac{\partial A}{\partial y} =\cos y$ and $ \dfrac{\partial B}{\partial x}=\cos y$
Thus, the vector field $F$ is conservative.
