MHT CET · Maths · Limits
\(\lim _{x \rightarrow \pi / 2}(\sec x-\tan x)\) is equal to
- A 2
- B \(-1\)
- C 1
- D 0
Answer & Solution
Correct Answer
(D) 0
Step-by-step Solution
Detailed explanation
\(\lim _{x \rightarrow \frac{\pi}{2}}(\sec x-\tan x)\)
\(\Rightarrow \quad \lim _{x \rightarrow \frac{\pi}{2}}\left(\frac{1-\sin x}{\cos x}\right) \quad\left(\frac{0}{0}\right.\) form \()\)
Using 'L' hospital rule, \(\Rightarrow \quad \lim _{x \rightarrow \frac{\pi}{2}} \frac{-\cos x}{-\sin x}\)
\(=\lim _{x \rightarrow \frac{\pi}{2}} \cot x=\cot \frac{\pi}{2}=0\)
\(\Rightarrow \quad \lim _{x \rightarrow \frac{\pi}{2}}\left(\frac{1-\sin x}{\cos x}\right) \quad\left(\frac{0}{0}\right.\) form \()\)
Using 'L' hospital rule, \(\Rightarrow \quad \lim _{x \rightarrow \frac{\pi}{2}} \frac{-\cos x}{-\sin x}\)
\(=\lim _{x \rightarrow \frac{\pi}{2}} \cot x=\cot \frac{\pi}{2}=0\)
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