20. Find the value of $\frac{1}{\sin 10^{\circ}}-4 \sin 70^{\circ}$.
20. Ans: 2
$$
\begin{aligned}
\frac{1}{\sin 10^{\circ}}-4 \sin 70^{\circ} & =\frac{1-4 \sin 70^{\circ} \sin 10^{\circ}}{\sin 10^{\circ}} \\
& =\frac{1-2\left(\cos 60^{\circ}-\cos 80^{\circ}\right)}{\sin 10^{\circ}} \\
& =\frac{1-2\left(\frac{1}{2}-\cos 80^{\circ}\right)}{\sin 10^{\circ}} \\
& =\frac{2 \cos 80^{\circ}}{\sin 10^{\circ}} \\
& =\frac{2 \sin 10^{\circ}}{\sin 10^{\circ}} \\
& =2 .
\end{aligned}
$$

Here we have used the formula:
$$
\sin A \sin B=\frac{\cos (A-B)-\cos (A+B)}{2} .
$$