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The terms tan ⁡ 80 o ,   tan ⁡ 70 o + tan ⁡ 10 o and tan ⁡ 10 o are in

Options

  1. Aarithmetic progression
  2. Bgeometric progression
  3. Charmonic progression
  4. DNone of these

Correct answer

A. arithmetic progression

Step-by-step solution

tan ⁡ 80 o = tan ⁡ 7 0 o + 1 0 o = tan ⁡ 70 o + tan ⁡ 10 o 1 - tan ⁡ 70 o tan ⁡ 10 o ⇒ tan ⁡ 80 o - tan ⁡ 80 o tan ⁡ 70 o tan ⁡ 10 o = tan ⁡ 70 o + tan ⁡ 10 o ⇒ tan ⁡ 80 o - tan ⁡ 80 o tan ⁡ 70 o cot ⁡ 80 o = tan ⁡ 70 o + tan ⁡ 10 o ⇒ tan ⁡ 80 o = 2 tan ⁡ 70 o + tan ⁡ 10 o ⇒ tan ⁡ 80 o + tan ⁡ 10 o = 2 tan ⁡ 70 o + tan ⁡ 10 o ⇒ they are in A . P .

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