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If tan 25 o = a , then the value of tan ⁡ 205 o - tan ⁡ 115 o tan ⁡ 245 o + tan ⁡ 335 o in terms of a is

Options

  1. A1 - a 2 1 + a 2
  2. B1 - a 2 a
  3. C2 a 1 + a 2
  4. D1 + a 2 1 - a 2

Correct answer

D. 1 + a 2 1 - a 2

Step-by-step solution

tan ⁡ 205 o - tan ⁡ 115 o tan ⁡ 245 o + tan ⁡ 335 o = tan ⁡ 25 o + cot ⁡ 25 o cot ⁡ 25 o - tan ⁡ 25 o = tan 2 ⁡ 25 o + 1 1 - tan 2 ⁡ 25 o = a 2 + 1 1 - a 2 = 1 + a 2 1 - a 2

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