The minimum value of $3 \cos x + 4 \sin x + 5$ is

If $\alpha+\beta+\gamma=2 \theta$,then $\cos \theta+\cos (\theta-\alpha)+\cos (\theta-\beta)+\cos (\theta-\gamma)$ is equal to

The maximum value of $\sin x - \cos x$ is equal to

If $A + B + C = \pi ,$ then $\frac{\cos A}{\sin B \sin C} + \frac{\cos B}{\sin C \sin A} + \frac{\cos C}{\sin A \sin B} = $

If $ABC$ is not a right-angled triangle and $\sin \left(\frac{\pi}{4}-A\right) \sin \left(\frac{\pi}{4}-B\right) = -\frac{1}{2 \sqrt{2}} \operatorname{cosec}\left(\frac{\pi}{4}-C\right)$,then $\tan A \tan B + \tan B \tan C + \tan C \tan A = $

The number of integral value$(s)$ of $p$ for which the equation $99 \cos 2\theta - 20 \sin 2\theta = 20p + 35$ will have a solution is: