$$ \begin{aligned} & \left(4 \cos ^2 \frac{\pi}{20}-1\right)\left(4 \cos ^2 \frac{3 \pi}{20}-1\right) \\ & \left(4 \cos ^2 \frac{5 \pi}{20}+1\right)\left(4 \cos ^2 \frac{7 \pi}{20}-1\right)\left(4 \cos ^2 \frac{9 \pi}{20}-1\right)= \end{aligned} $$

If $A$ and $B$ are the values such that $(A+B)$ and $(A-B)$ are not odd multiples of $\frac{\pi}{2}$ and $2 \tan (A+B)=3 \tan (A-B)$, then $\sin A \cos A=$

If $\cos ^3 80^{\circ}+\cos ^3 40^{\circ}-\cos ^3 20^{\circ}=k$, then $\frac{4 k}{3}=$

$$ \cos 13^{\circ} \sin 17^{\circ} \sin 21^{\circ} \cos 47^{\circ}= $$