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If tan π 9 , x , tan 7 π 18 are in arithmetic progression and tan π 9 , y , tan 5 π 18 are also in arithmetic progression, then | x - 2 y | is equal to :

Options

  1. A4
  2. B3
  3. C0
  4. D1

Correct answer

C. 0

Step-by-step solution

x = 1 2 tan π 9 + tan 7 π 18 and 2 y = tan π 9 + tan 5 π 18 so, x - 2 y = 1 2 tan π 9 + tan 7 π 18 - tan π 9 + tan 5 π 18 ⇒ | x - 2 y | = cot π 9 - tan π 9 2 - tan 5 π 18 = cot 2 π 9 - cot 2 π 9 = 0 astan 5 π 18 = cot 2 π 9 ; tan 7 π 18 = cot π 9

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