When the function $f(x) = 2(\cos 3x + \cos \sqrt{3} x)$ attains its maximum value,what is the number of values of $x$?

If $\cos A \sin \left( A - \frac{\pi}{6} \right)$ is maximum,then the value of $A$ is equal to

Let $f(x) = \cos 5x + A \cos 4x + B \cos 3x + C \cos 2x + D \cos x + E$,and $T = f(0) - f\left(\frac{\pi}{5}\right) + f\left(\frac{2\pi}{5}\right) - f\left(\frac{3\pi}{5}\right) + \dots + f\left(\frac{8\pi}{5}\right) - f\left(\frac{9\pi}{5}\right)$. Then,$T$

If $A>0, B>0$ and $A+B=\frac{\pi}{3}$,then the maximum value of $\tan A \tan B$ is

In $\Delta ABC$,the minimum value of $\frac{\sum \cot^2 \frac{A}{2} \cot^2 \frac{B}{2}}{\prod \cot^2 \frac{A}{2}}$ is

Assertion $(A)$: If $\alpha=12^{\circ}, \beta=15^{\circ}, \gamma=18^{\circ}$,then $\tan 2 \alpha \tan 2 \beta+\tan 2 \beta \tan 2 \gamma+\tan 2 \gamma \tan 2 \alpha=1$.
Reason $(R)$: In $\triangle ABC$,$\tan \frac{A}{2} \tan \frac{B}{2}+\tan \frac{B}{2} \tan \frac{C}{2}+\tan \frac{C}{2} \tan \frac{A}{2}=1$.
Which of the following is true?