#### Answer

$\lim_{x\to\pi/4}3\csc2x\cot2x=0$

#### Work Step by Step

$\lim_{x\to\pi/4}3\csc2x\cot2x$
Evaluate this limit applying direct substitution:
$\lim_{x\to\pi/4}3\csc2x\cot2x=3\csc\Big[2\Big(\dfrac{\pi}{4}\Big)\Big]\cot\Big[2\Big(\dfrac{\pi}{4}\Big)\Big]=...$
$...=3\csc\dfrac{\pi}{2}\cot\dfrac{\pi}{2}=3(1)(0)=0$