Answer
The solution is:
$$\lim_{x\to\pi/2}\frac{2\tan x}{\sec^2 x}=0.$$
Work Step by Step
To solve this limit follow the steps below:
$$\lim_{x\to\pi/2}\frac{2\tan x}{\sec^2 x}=\lim_{x\to\pi/2}\frac{2\frac{\sin x}{\cos x}}{\frac{1}{\cos^2 x}}=\lim_{x\to\pi/2}\frac{2\sin x\cos^2 x}{\cos x}=\lim_{x\to\pi/2}2\sin x\cos x=2\sin(\pi/2)\cos(\pi/2)=2\cdot1\cdot0=0.$$
