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AP EAMCET201825 Apr 2018Morning ShiftMathematicsProperties of TrianglesActual

With the usual notations, in a ∆ A B C , if a = 2 , b = 6 and c = 3 + 1 , then sin 2 C - sin 2 A =

Options

  1. A1 + 3 4
  2. B3 2
  3. C3 4
  4. D3 4

Correct answer

C. 3 4

Step-by-step solution

We have, a = 2 ,   b = 6 and c = 3 + 1 Using cosine rule, we get, cos C = a 2 + b 2 - c 2 2 a b = 6 - 2 3 4 6 = 3 - 1 2 2 And cos A = c 2 + b 2 - a 2 2 c b = 4 + 2 3 + 6 - 4 2 3 + 1 6 = 1 2 Now, sin 2 C - sin 2 A = 1 - cos 2 C - 1 - cos 2 A = cos 2 A - cos 2 C = 1 2 - 3 - 1 2 2 2 = 1 2 - 4 - 2 3 8 = 3 4 .

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