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AP EAMCET202124 Aug 2021Morning ShiftMathematicsTrigonometric Ratios & IdentitiesActual

In a A B C, 2 a c 1 2 (A-B+C) is equal to

Options

  1. Aa^2+b^2+c^2
  2. Ba^2+b^2-c^2
  3. Ca^2+c^2-b^2
  4. Db^2+c^2-a^2

Correct answer

C. a^2+c^2-b^2

Step-by-step solution

aligned & In a A B C & A+B+C=180^ & Then, 2 a c 1 2 (A-B+C) & 2 a c 1 2 (180-B-B) [ A+C=180^ -B ] & 2 a c (90^ -B ) & =2 a c B [ (90- )= ] & =2 a c a^2+c^2-b^2 2 a c [ B= a^2+c^2-b^2 2 a c ] & =a^2+c^2-b^2 aligned

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