COMEDK · Maths · 16. Limits
\(\lim _{x \rightarrow \dfrac{\pi}{4}} \dfrac{\sec ^2 x-2}{\tan x-1}=\)
- A 1
- B \(\sqrt{2}\)
- C \(\dfrac{1}{\sqrt{2}}\)
- D 2
Answer & Solution
Correct Answer
(D) 2
Step-by-step Solution
Detailed explanation
Given the limit \(L = \lim _{x \rightarrow \dfrac{\pi}{4}} \dfrac{\sec ^2 x-2}{\tan x-1}\). Using the identity \(\sec ^2 x = 1 + \tan ^2 x\), the expression becomes: \(L = \lim _{x \rightarrow \dfrac{\pi}{4}} \dfrac{1 + \tan ^2 x - 2}{\tan x - 1}\)…
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