If the orthocentre and circumcentre of a triangle $ABC$ are at equal distances from the side $BC$ and lie on the same side of $BC$,then the value of $\tan B \tan C$ is equal to:

If $e^{\sin x}-e^{-\sin x}-4=0,$ then the number of real values of $x$ is

The value of $\cos 52^\circ + \cos 68^\circ + \cos 172^\circ$ is

If $\tan \theta + \cot \theta = 4$,then $\tan^{4} \theta + \cot^{4} \theta = $

The value of the expression $\frac{1+\sin 2 \alpha}{\cos (2 \alpha-2 \pi) \tan \left(\alpha-\frac{3 \pi}{4}\right)} - \frac{1}{4} \sin 2 \alpha \left[\cot \frac{\alpha}{2}+\cot \left(\frac{3 \pi}{2}+\frac{\alpha}{2}\right)\right]$ is:

Assertion $(A)$: If $\sqrt{4 \sin^4 \theta + \sin^2 2\theta} + 4 \cos^2\left(\frac{\pi}{4} - \frac{\theta}{2}\right) = 2$,then $\theta$ lies in the $3^{\text{rd}}$ quadrant or $4^{\text{th}}$ quadrant.
Reason $(R)$: $\sqrt{\sin^2 \theta} = \sin \theta$