Question

Evaluate :

$\underset{x\to \frac{\pi }{4}}{lim}\frac{{\sec }^{2}x-2}{\tan x-1}$

• A. $\frac{1}{4}$
• B. $1$
• C. $\frac{1}{2}$
• D. $2$

Answer 1

Answer: (D)

$2$

$\underset{x\to \frac{\pi }{4}}{lim}\frac{{\sec }^{2}x-2}{\tan x-1}$

$=\underset{x\to \frac{\pi }{4}}{lim}\frac{1+{\tan }^{2}x-2}{\tan x-1}$

$=\underset{x\to \frac{\pi }{4}}{lim}(\tan x+1)=2$