PrepRung
Sign inSign up free

NDA 2017 Maths · Mathematics · Trigonometric Functions and Identities · hard

The value of cos (π)/(7)cos (2π)/(7)cos (4π)/(7) is

Single correct option

The value of cos⁡π7cos⁡2π7cos⁡4π7\cos\dfrac\pi7\cos\dfrac{2\pi}7\cos\dfrac{4\pi}7 is
  1. A. 18\dfrac18
  2. B. −14-\dfrac14
  3. C. 116\dfrac1{16}
  4. D. −18-\dfrac18
Show answer and solution

Answer: (D) −18-\dfrac18

Multiply and divide by sin⁡π7\sin\frac\pi7 and use sin⁡2θ=2sin⁡θcos⁡θ\sin2\theta=2\sin\theta\cos\theta three times: the product is sin⁡(8π/7)8sin⁡(π/7)\frac{\sin(8\pi/7)}{8\sin(\pi/7)}. Since sin⁡8π7=−sin⁡π7\sin\frac{8\pi}7=-\sin\frac\pi7, the value is −18-\frac18. Missing the sign is the trap.
Report a mistake

Original question written in the NDA 2017 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