The value of $\left(1+\cos \frac{\pi}{8}\right)\left(1+\cos \frac{3 \pi}{8}\right)\left(1+\cos \frac{5 \pi}{8}\right)\left(1+\cos \frac{7 \pi}{8}\right)$ is

If $\alpha+\beta=\frac{\pi}{2}$ and $\beta+\gamma=\alpha$, then $\tan \alpha$ equals

If $\mathrm{A}>\mathrm{B}$ and $\tan \mathrm{A}-\tan \mathrm{B}=x$ and $\cot \mathrm{B}-\cot \mathrm{A}=y$, then $\cot (\mathrm{A}-\mathrm{B})=$

The value of the expression $\sqrt{3} \operatorname{cosec} 20^{\circ}-\sec 20^{\circ}$ is equal to