Eccentricity of the curve represented by $x=4(\cos t+\sin t)\&y=\sqrt{7}(\cos t-\sin t)$ is given by 

Here $\frac{x}{4}=\cos t+\sin t and\frac{y}{\sqrt{7}}=\cos t-\sin t$

Square and adding equation (1) and (2) $\frac{x^2}{16}+\frac{y^2}{7}=2({\sin }^{2}t+{\cos }^{2}t), \Rightarrow \frac{x^2}{32}+\frac{y^2}{14}=1,$ which is an ellipse eccentricity $e=\sqrt{1-\frac{b^2}{a^2}}=\sqrt{1-\frac{14}{32}}=\frac{3}{4}$