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

Let $\alpha$ and $\beta$ be two real roots of the equation $(k+1) \tan ^2 x-\sqrt{2} \lambda \tan x=(1-k)$ where $k(\neq-1)$ and $\lambda$ are real numbers. If $\tan ^2(\alpha+\beta)=50$, then a value of $\lambda$ is