In a triangle,if $\tan A + \tan B + \tan C = 6$ and $\tan A \tan B = 2$,then the values of $\tan A, \tan B,$ and $\tan C$ are:

If $\alpha, \beta, \gamma$ are positive numbers such that $\alpha + \beta = \pi$ and $\beta + \gamma = \alpha$,then $\tan \alpha$ is equal to - (where $\gamma \neq n\pi, n \in I$)

If $A + B + C = \frac{3\pi}{2},$ then $\cos 2A + \cos 2B + \cos 2C = $

Let $a = \max_{x \in R} \{8^{2 \sin 3x} \cdot 4^{4 \cos 3x}\}$ and $\beta = \min_{x \in R} \{8^{2 \sin 3x} \cdot 4^{4 \cos 3x}\}$. If $8x^2 + bx + c = 0$ is a quadratic equation whose roots are $\alpha^{1/5}$ and $\beta^{1/5}$,then the value of $c - b$ is equal to:

Find the maximum and minimum values of the function given by $h(x) = \sin(2x) + 5$.

The value of $5 \cos \theta + 3 \cos \left(\theta + \frac{\pi}{3}\right) + 3$ lies between