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AP EAMCET20224 Jul 2022Morning ShiftMathematicsProperties of TrianglesActual

In a triangle A B C , if a ≠ b , a cos A - b cos B a cos B - b cos A + cos C =

Options

  1. A0
  2. B1
  3. C2
  4. D- 1

Correct answer

A. 0

Step-by-step solution

Given, Triangle A B C , To find the value of a cos A - b cos B a cos B - b cos A + cos C Using the sine rule we get, = 2 R sin A cos A - 2 R sin B cos B 2 R sin A cos B - 2 R sin B cos A + cos C = sin 2 A - sin 2 B 2 sin A cos B - sin B cos A + cos C = 2 sin A - B cos A + B 2 sin A - B + cos C = cos A + B + cos C = - cos C + cos C   as   A + B = π - C = 0

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