The minimum and maximum values of $\cos \left(x+\frac{\pi}{3}\right)+2 \sqrt{2} \sin \left(x+\frac{\pi}{3}\right)$ are respectively

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:

The minimum value of the function $f(x) = 2\cos 2x - \cos 4x$ in the interval $0 \le x \le \pi$ is:

The sum of all the integral values of $p$ such that the equation $3\sin^2 x + 12\cos x - 3 = p, x \in R$ has at least one solution, is:

If $A + B = \pi / 2$,then the maximum value of $\cos A \cos B$ is:

If $A+B+C=4S$,then $\cos (2S-A)+\cos (2S-B)-\cos (2S-C)-\cos 2S=$