Find the value of $\tan 4^{\circ} \tan 43^{\circ} \tan 47^{\circ} \tan 86^{\circ}$.

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 $\theta$ is an acute angle and $\sin\theta = \frac{p - 6}{8 - p}$,then $p$ must satisfy:

If $A = \sin^2 x + \cos^4 x$,then for all real $x :$

If $\tan \theta - \cot \theta = 0$ and $\theta$ is a positive acute angle,then the value of $\frac{\tan (\theta + 15^{\circ})}{\tan (\theta - 15^{\circ})}$ is

$\frac{{\sin (B + A) + \cos (B - A)}}{{\sin (B - A) + \cos (B + A)}} = $