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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Trigonometric Ratios & Identities

NDA 2023 · Mathematics · Trigonometric Ratios & Identities

Let p= ((π)/(5)) ((2 π)/(5)) and q= ((4 π)/(5)) ((8 π)/(5)). What...

Let p=cos⁡(π5)cos⁡(2π5)p=\cos \left(\frac{\pi}{5}\right) \cos \left(\frac{2 \pi}{5}\right)and q=\cos \left(\frac{4 \pi}{5}\right) \cos\left(\frac{8 \pi}{5}\right).WhatisthevalueofWhat is the value ofp+q$?

Options

  1. A−12-\frac{1}{2}
  2. B−14-\frac{1}{4}
  3. C0
  4. D12\frac{1}{2}

Correct answer

C. 0

Step-by-step solution

 Since, p+q=cos⁡(π5)⋅cos⁡(2π5)+cos⁡(4π5)⋅cos⁡(8π5)=cos⁡(π5)⋅cos⁡(2π5)−cos⁡(π5)⋅cos⁡(2π5)=0\begin{aligned} & \text{ Since, } p+q \\ & =\cos \left(\frac{\pi}{5}\right) \cdot \cos \left(\frac{2 \pi}{5}\right)+\cos \left(\frac{4 \pi}{5}\right) \cdot \cos \left(\frac{8 \pi}{5}\right) \\ & =\cos \left(\frac{\pi}{5}\right) \cdot \cos \left(\frac{2 \pi}{5}\right)-\cos \left(\frac{\pi}{5}\right) \cdot \cos \left(\frac{2 \pi}{5}\right)=0\end{aligned}
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