If $A + B + C = 180^\circ$,then $\frac{\tan A + \tan B + \tan C}{\tan A \cdot \tan B \cdot \tan C} = $

The value of $x$ for the maximum value of $(\sqrt{3} \sin x + \cos x)$ is .....$^o$.

Let $a$ be the maximum value of $(3 \cos \theta - 4 \sin \theta)$ and $\theta \neq \frac{n \pi}{2}$. If $\alpha = a \sin^2 \theta \cos^3 \theta$ and $\beta = a \sin^3 \theta \cos^2 \theta$,then $\sqrt{\frac{(\alpha^2 + \beta^2)^5}{(\alpha \beta)^4}} = $

The maximum value of $\sin(x + \pi/6) + \cos(x + \pi/6)$ is attained at $x =$

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

If $p$ and $q$ are positive numbers such that $p^2 + q^2 = 1$,then the maximum value of $p + q$ is: