The value of $\cos 1^{\circ} \cos 2^{\circ} \cos 3^{\circ} \ldots \cos 179^{\circ} = $

The value of $\sqrt{2+\sqrt{2(1+\cos 4A)}}$ is equal to

$\sin^{2} \theta = \frac{(x+y)^{2}}{4xy}$ is possible only when

If $\sqrt{2} \tan 2 \theta = \sqrt{6}$ and $0^{\circ} < \theta < 45^{\circ},$ then the value of $\sin \theta + \sqrt{3} \cos \theta - 2 \tan^{2} \theta$ is

If $\sin \theta_1 + \sin \theta_2 + \sin \theta_3 = 3,$ then $\cos \theta_1 + \cos \theta_2 + \cos \theta_3 =$

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