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AP EAMCET20224 Jul 2022Evening ShiftMathematicsProperties of TrianglesActual

In any triangle A B C , b + c cos A + c + a cos B + a + b cos C equals

Options

  1. A0
  2. Ba + b + c
  3. Ca + b - c
  4. Da - b - c

Correct answer

B. a + b + c

Step-by-step solution

Given b + c cos A + c + a cos B + a + b cos C = b cos A + c cos A + c cos B + a cos B + a cos C + b cos C = b cos A + a cos B + c cos A + a cos C + c cos B + b cos C     . . . 1 By projection formula, we have a = b cos C + c cos B Therefore, from 1 , we have = a + b + c

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