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JEE Main202312 Apr 2023Morning ShiftMathematicsStraight LinesActual

In a triangle A B C , if cos A + 2 cos B + cos C = 2 and the lengths of the sides opposite to the angles A and C are 3 and 7 respectively, then cos A - cos C is equal to

Options

  1. A9 7
  2. B10 7
  3. C5 7
  4. D3 7

Correct answer

B. 10 7

Step-by-step solution

Given, A B = 7 ,   B C = 3 . ⇒ c = 7 ,   a = 3 . Apply cosine rule in the given equation cos A + 2 cos B + cos C = 2 , we get ⇒ b 2 + c 2 - a 2 2 b c + 2 c 2 + a 2 - b 2 2 a c + a 2 + b 2 - c 2 2 a b = 2 ⇒ b 2 + 49 - 9 14 b + 49 + 9 - b 2 21 + 9 + b 2 - 49 6 b = 2 ⇒ b 2 + 40 14 b + 58 - b 2 21 + b 2 - 40 6 b = 2 ⇒ b 3 - 5 b 2 - 16 b + 80 = 0 ⇒ b - 4 b + 4 b - 5 = 0 ⇒ b = - 4 , 4 , 5 . But b ≠ - 4 . Also, if b = 4 triangle cannot be constructed. That means b

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