$(\cos A+\sin A{)}^2-(\cos A-\sin A{)}^2$ is equal to

Expanding the given expression we get

$(\cos A+\sin A){}^2-(\cos A+\sin A){}^2$

$=\cos A{}^2+\sin A{}^2+2\cos A\sin A-(\cos A{}^2+\sin A{}^2-2\cos A\sin A)$

$=2(2\cos A\sin A)$

$=4\cos A\sin A$

Hence, option D is correct.