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AP EAMCET202119 Aug 2021Evening ShiftMathematicsProperties of TrianglesActual

In triangle A B C , a + b + c B C + A B + a + b + c A C + A B = 3 then tan C 8 =

Options

  1. A6 + 3 + 2 − 2
  2. B6 − 3 − 2 + 2
  3. C6 − 3 + 2 − 2
  4. D6 + 3 − 2 + 2

Correct answer

C. 6 − 3 + 2 − 2

Step-by-step solution

Given, a + b + c B C + A B + a + b + c A C + A B = 3 Here, B C = a ,   A C = b ,   A B = c . Then, a + b + c a + c + a + b + c b + c = 3 ⇒ a + c a + c + b a + c + b + c b + c + a b + c = 3 ⇒ 1 + b a + c + 1 + a b + c = 3 ⇒ b a + c + a b + c = 1 ⇒ b 2 + b c + a 2 + a c = a b + a c + b c + c 2 ⇒ b 2 + a 2 - c 2 a b = 1 ⇒ b 2 + a 2 - c 2 2 a b = 1 2 Now from Cosine rule, we know b 2 + a 2 - c 2 2 a b = cos C ⇒ cos C = 1 2 ⇒ C = π 3 Now, tan C 8 = tan &#960

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