Q79 / 120 · NDA 2024 (Phase 2) · Mathematics

What is $\lim (\sec \theta-\tan \theta)$ equal to? $x \rightarrow \frac{\pi}{2}$

  • A
    $-1$
  • Correct answer
    B
    $0$
  • C
    $\frac{1}{2}$
  • D
    $1$

Solution

$\begin{aligned} & \text { } \lim _{\theta \rightarrow \frac{\pi}{2}}(\sec \theta-\tan \theta) \\ & \lim _{\theta \rightarrow \frac{\pi}{2}}(\sec \theta-\tan \theta)=\lim _{\theta \rightarrow \frac{\pi}{2}} \frac{1-\sin \theta}{\cos \theta}\left(\frac{0}{0} \text { form }\right) \\ & \lim _{\theta \rightarrow \frac{\pi}{2}}\left(\frac{-\cos \theta}{-\sin \theta}\right)=0 \text { (Using L Hospital Rule) }\end{aligned}$

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

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