Q223 / 270 · NDA 2023 (Phase 2) · Mathematics

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

  • A
    $-\frac{1}{2}$
  • B
    $-\frac{1}{4}$
  • Correct answer
    C
    0
  • D
    $\frac{1}{2}$

Solution

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

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

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