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

If $\sin (\theta-\alpha), \sin \theta$ and $\sin (\theta+\alpha)$ are in H.P., then the value of $\cos ^2 \theta$ is