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

If $\tan x=\frac{3}{4}$ and $\pi< x< \frac{3 \pi}{2}$, then $\cos \frac{x}{2}=$ ___________

The approximate value of $\cos \left(30^{\circ}, 30^{\prime}\right)$ is given that $1^{\circ}=0.0175^{\circ}$ and $\cos 30^{\circ}=0.8660$