Solution:

(i) It is given that functions can be written as

$\sin ^{-1}\left(\frac{\sqrt{3}-1}{2 \sqrt{2}}\right)=\sin ^{-1}\left(\frac{\sqrt{3}}{2 \sqrt{2}}-\frac{1}{2 \sqrt{2}}\right)
$Taking $1 / \mathrm{v} 2$ as common from the above equation we obtain,
$=\sin ^{-1}\left(\frac{\sqrt{3}}{2} \times \frac{1}{\sqrt{2}}-\frac{1}{2} \times \frac{1}{\sqrt{2}}\right)$
Taking $\mathrm{v} 3 / 2$ as common, and $1 / \mathrm{v} 2$ from the above equation we obtain,
$=\sin ^{-1}\left(\frac{\sqrt{3}}{2} \times \sqrt{1-\left(\frac{1}{\sqrt{2}}\right)^{2}}-\frac{1}{\sqrt{2}} \times \sqrt{1-\left(\frac{\sqrt{3}}{2}\right)^{2}}\right)$
On simplifying, we obtain
$=\sin ^{-1}\left(\frac{\sqrt{3}}{2}\right)-\sin ^{-1}\left(\frac{1}{\sqrt{2}}\right)$
By substituting the values we have,
$=\frac{\pi}{3}-\frac{\pi}{4}$
Taking LCM and cross multiplying we obtain,
$=\frac{\pi}{12}$

(ii) We can write the given question as
$\sin ^{-1}\left(\frac{\sqrt{3}+1}{2 \sqrt{2}}\right)=\sin ^{-1}\left(\frac{\sqrt{3}}{2 \sqrt{2}}+\frac{1}{2 \sqrt{2}}\right)$
Taking $1 / \mathrm{v} 2$ as common from the above equation we obtain
$=\sin ^{-1}\left(\frac{\sqrt{3}}{2} \times \frac{1}{\sqrt{2}}+\frac{1}{2} \times \frac{1}{\sqrt{2}}\right)$
Taking $\mathrm{V} 3 / 2$ as common, and $1 / \mathrm{v} 2$ from the above equation we obtain,
$=\sin ^{-1}\left(\frac{\sqrt{3}}{2} \times \sqrt{1-\left(\frac{1}{\sqrt{2}}\right)^{2}}+\frac{1}{\sqrt{2}} \times \sqrt{1-\left(\frac{\sqrt{3}}{2}\right)^{2}}\right)$
On simplifying we obtain,
$=\sin ^{-1}\left(\frac{\sqrt{3}}{2}\right)+\sin ^{-1}\left(\frac{1}{\sqrt{2}}\right)$
Substituting the corresponding values we obtain
$\begin{array}{l}
=\frac{\pi}{3}+\frac{\pi}{4} \\
=\frac{7 \pi}{12}
\end{array}$