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NDA 2022
Exam
NDA
Year
2022
Subject
Mathematics
Chapter
Trigonometric Ratios & Identities

NDA 2022 · Mathematics · Trigonometric Ratios & Identities

What is the value of cosec (-(73 π)/(3))?

What is the value of $\operatorname{cosec} \left(-\frac{73 \pi}{3}\right)?

Options

  1. A23\frac{2}{\sqrt{3}}
  2. B−23-\frac{2}{\sqrt{3}}
  3. C22
  4. D−2-2

Correct answer

B. −23-\frac{2}{\sqrt{3}}

Step-by-step solution

cosec⁡(−73π3)=−cosec⁡(73π3)=−cosec⁡(24π+π3)=−cosec⁡π3=−23\begin{aligned} & \operatorname{cosec}\left(-\frac{73 \pi}{3}\right)=-\operatorname{cosec}\left(\frac{73 \pi}{3}\right) \\ & =-\operatorname{cosec}\left(24 \pi+\frac{\pi}{3}\right)=-\operatorname{cosec} \frac{\pi}{3}=-\frac{2}{\sqrt{3}}\end{aligned}
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