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NDA 2019 Maths · Mathematics · Trigonometric Functions and Identities · hard

The value of cos (π)/(5)cos (2π)/(5) is

Single correct option

The value of cos⁡π5cos⁡2π5\cos\dfrac\pi5\cos\dfrac{2\pi}5 is
  1. A. 18\dfrac18
  2. B. 12\dfrac12
  3. C. 14\dfrac14
  4. D. 54\dfrac{\sqrt5}{4}
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Answer: (C) 14\dfrac14

Multiply and divide by sin⁡π5\sin\dfrac\pi5: 2sin⁡π5cos⁡π5cos⁡2π52sin⁡π5=sin⁡2π5cos⁡2π52sin⁡π5=sin⁡4π54sin⁡π5\dfrac{2\sin\frac\pi5\cos\frac\pi5\cos\frac{2\pi}5}{2\sin\frac\pi5}=\dfrac{\sin\frac{2\pi}5\cos\frac{2\pi}5}{2\sin\frac\pi5}=\dfrac{\sin\frac{4\pi}5}{4\sin\frac\pi5}. Since sin⁡4π5=sin⁡π5\sin\dfrac{4\pi}5=\sin\dfrac\pi5, the value is 14\dfrac14. Using three cosines would give 18\dfrac18, which is not asked here.
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Original question written in the NDA 2019 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake