The extremum values of the function $f(x) = \frac{1}{\sin x + 4} - \frac{1}{\cos x - 4}$ for $x \in R$ are:

If $x \in (0, \frac{\pi}{4})$,then the expression $\frac{\cos x}{\sin^2 x(\cos x - \sin x)}$ cannot take which of the following values?

If $y = \log_2 \sin x$, then the minimum value of $\cosh y$ is

If $A = \sin^2 \theta + \cos^4 \theta$,then for all values of $\theta$,$A$ lies in the interval

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?

If $A+B+C=\frac{\pi}{4}$,then $\sin 4A+\sin 4B+\sin 4C=$