Solution:

Option(B)
To find: Value of $\left|\begin{array}{cc}\cos 70^{\circ} & \sin 20^{\circ} \\ \sin 70^{\circ} & \cos 20^{\circ}\end{array}\right|$
Formula used: (i) $\cos \theta=\sin (90-\theta)$
We have, $\left|\begin{array}{cc}\cos 70^{\circ} & \sin 20^{\circ} \\ \sin 70^{\circ} & \cos 20^{\circ}\end{array}\right|$
On expanding the above,
$\Rightarrow\left\{\cos 70^{\circ}\right\}\left\{\cos 20^{\circ}\right\}-\left\{\sin 70^{\circ}\right\}\left\{\sin 20^{\circ}\right\}$
On applying formula $\cos \theta=\sin (90-\theta)$
$\begin{array}{l}
\Rightarrow\{\sin (90-70)\}\{\sin (90-20)\}-\left\{\sin 70^{\circ}\right\}\left\{\sin 20^{\circ}\right\} \\
\Rightarrow\left\{\sin 20^{\circ}\right\}\left\{\sin 70^{\circ}\right\}-\left\{\sin 70^{\circ}\right\}\left\{\sin 20^{\circ}\right\} \\
=0
\end{array}$