$\tan 1^\circ \tan 2^\circ \tan 3^\circ \tan 4^\circ \dots \tan 89^\circ = $

If $x = r \cos \theta \cos \phi$,$y = r \cos \theta \sin \phi$,and $z = r \sin \theta$,then the value of $x^{2} + y^{2} + z^{2}$ is

In the graph of the function $\sqrt{3} \sin x + \cos x$,the maximum distance of a point from the $x$-axis is:

Let $f(x) = \max (\sin x, \cos x)$ and $g(x) = \min (\cos x, \sin x)$. If the equation $f(x)y^2 + ay + g(x) = 0$ has real roots for all $x \in R$,then the complete set of values of $a$ is:

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 $x = y \cos \frac{2\pi}{3} = z \cos \frac{4\pi}{3}$,then $xy + yz + zx = $