If $\frac{\sin A - \sin C}{\cos C - \cos A} = \cot B,$ then $A, B, C$ are in

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

In a $\Delta ABC$,$\angle B = \frac{\pi}{3}$,$\angle C = \frac{\pi}{4}$ and $D$ divides $BC$ internally in the ratio $1:3$,then $\frac{\sin \angle BAD}{\sin \angle CAD}$ is equal to

If $180^{\circ} < \theta < 270^{\circ},$ then the value of $\sqrt{4 \sin^{4} \theta + \sin^{2} 2\theta} + 4 \cos^{2} \left(\frac{\pi}{4} - \frac{\theta}{2}\right)$ is

If $\tan \theta = \frac{p}{q},$ then $\frac{p \sin \theta - q \cos \theta}{p \sin \theta + q \cos \theta} = $

Given that $\pi < \alpha < \frac{3\pi}{2},$ then the expression $\sqrt{4\sin^4 \alpha + \sin^2 2\alpha} + 4\cos^2 \left( \frac{\pi}{4} - \frac{\alpha}{2} \right)$ is equal to