Q81 / 150 · MHT CET 2012 · Mathematics

$\lim _{x \rightarrow \pi / 2}(\sec x-\tan x)$ is equal to

  • A
    2
  • B
    $-1$
  • C
    1
  • Correct answer
    D
    0

Solution

$\lim _{x \rightarrow \frac{\pi}{2}}(\sec x-\tan x)$ $\Rightarrow \quad \lim _{x \rightarrow \frac{\pi}{2}}\left(\frac{1-\sin x}{\cos x}\right) \quad\left(\frac{0}{0}\right.$ form $)$ Using 'L' hospital rule, $\Rightarrow \quad \lim _{x \rightarrow \frac{\pi}{2}} \frac{-\cos x}{-\sin x}$ $=\lim _{x \rightarrow \frac{\pi}{2}} \cot x=\cot \frac{\pi}{2}=0$

Hence, the correct answer is option: 'D'.

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