Question

evaluate the limit
...


​

Answer 1

Answer:

Here is your answer!!!!!!!!!!! ☺️☺️

Mark me as brainliest....

Answer 2

Answer:

$\large\boxed{\sf{2}}$

Step-by-step explanation:

$\displaystyle \lim_{x \to \frac{\pi}{4}} \frac{( { \sec }^{2} x - 2)}{( \tan x - 1) } \\ \\ = \displaystyle \lim_{x \to \frac{\pi}{4}} \frac{( { \tan }^{2}x + 1 - 2) }{( \tan x - 1) } \\ \\ = \displaystyle \lim_{x \to \frac{\pi}{4}} \frac{ ({ \tan}^{2} x - 1)}{( \tan x - 1) } \\ \\ = \displaystyle \lim_{x \to \frac{\pi}{4}} \frac{( \tan x + 1) \cancel{( \tan x - 1)} }{ \cancel{( \tan x - 1) }} \\ \\ = \displaystyle \lim_{x \to \frac{\pi}{4}} ( \tan x + 1) \\ \\ = \tan \frac{\pi}{4} + 1 \\ \\ = 1 + 1 \\ \\ = 2$

Concept Map:-

• ${ \sec }^{2} \alpha = 1 + { \tan}^{2} \alpha$

• $( {x}^{2} - {y}^{2} ) = (x + y)(x - y)$