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NDA 2024
Exam
NDA
Year
2024
Subject
Mathematics
Chapter
Limits

NDA 2024 · Mathematics · Limits

What is ( θ- θ) equal to? x arrow (π)/(2)

What is lim⁡(sec⁡θ−tan⁡θ)\lim (\sec \theta-\tan \theta) equal to? x→π2x \rightarrow \frac{\pi}{2}

Options

  1. A−1-1
  2. B00
  3. C12\frac{1}{2}
  4. D11

Correct answer

B. 00

Step-by-step solution

lim⁡θ→π2(sec⁡θ−tan⁡θ)lim⁡θ→π2(sec⁡θ−tan⁡θ)=lim⁡θ→π21−sin⁡θcos⁡θ(00 form )lim⁡θ→π2(−cos⁡θ−sin⁡θ)=0 (Using L Hospital Rule) \begin{aligned} & \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}
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