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The value of cos 2 π 7 + cos 4 π 7 + cos 6 π 7 is equal to

Options

  1. A- 1
  2. B- 1 2
  3. C- 1 3
  4. D- 1 4

Correct answer

B. - 1 2

Step-by-step solution

Given, cos 2 π 7 + cos 4 π 7 + cos 6 π 7 = 1 2 sin π 7 2 cos 2 π 7 sin π 7 + 2 cos 4 π 7 sin π 7 + 2 cos 6 π 7 sin π 7 = 1 2 sin π 7 sin 3 π 7 - sin π 7 + sin 5 π 7 - sin 3 π 7 + sin 7 π 7 - sin 5 π 7 Since, 2 cos A sin B = sin A + B - sin A - B = 1 2 sin π 7 - sin π 7 + sinπ = - 1 2 , ∵ sinπ = 0

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