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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Differentiation

NDA 2023 · Mathematics · Differentiation

What is the derivative of cosec (x^ ^ ) ?

What is the derivative of cosec⁡(x∘)?\operatorname{cosec} \left(x^{{}^{\circ}}\right) ?

Options

  1. A−cosec⁡(x∘)cot⁡(x∘)-\operatorname{cosec} \left(x^{{}^{\circ}}\right) \cot \left(x^{{}^{\circ}}\right)
  2. B−π180cosec⁡(x∘)cot⁡(x∘)-\frac{\pi}{180} \operatorname{cosec} \left(x^{{}^{\circ}}\right) \cot \left(x^{{}^{\circ}}\right)
  3. Cπ180cosec⁡(x∘)cot⁡(x∘)\frac{\pi}{180} \operatorname{cosec} \left(x^{{}^{\circ}}\right) \cot \left(x^{{}^{\circ}}\right)
  4. D−π180cosec⁡(x)cot⁡(x)-\frac{\pi}{180} \operatorname{cosec}(x) \cot (x)

Correct answer

B. −π180cosec⁡(x∘)cot⁡(x∘)-\frac{\pi}{180} \operatorname{cosec} \left(x^{{}^{\circ}}\right) \cot \left(x^{{}^{\circ}}\right)

Step-by-step solution

\frac{d}{d x} \operatorname{cosec}\left(x^{{}^{\circ}}\right)=\frac{d}{d x} \operatorname{cosec}\left(\frac{x \pi}{180}\right)=\frac{-\pi}{180} \operatorname{cosec}\left(\frac{\pi x}{180}\right) \cdot \cot \left(\frac{\pi x}{180}\right)=\frac{-\pi}{180} \operatorname{cosec} \left(x^{{}^{\circ}}\right)\cdot \cot\left( x^{{}^{\circ}}\right)
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