$(1-\sin A+\cos A{)}^2$ is equal to

Consider the following statements

$\mathrm{I}.$ $n\left\{{\sin }^2{\left(67\frac{1}{2}\right)}^{°}-{\sin }^2{\left(22\frac{1}{2}\right)}^{°}\right\}>1$ for all positive integers $n\ge 2$.

$\mathrm{II}.$ If $x$ is any positive real number, then $nx>1$ for all positive integers $n\ge 2$.

Which of the above statement(s) is/are correct?

If $\sin x+\sin y=a$ and $\cos x+\cos y=b,$ then ${\tan }^2\left(\frac{x+y}{2}\right)+{\tan }^2\left(\frac{x-y}{2}\right)$ is equal to