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AP EAMCET202125 Aug 2021Evening ShiftMathematicsProperties of TrianglesActual

In a A B C , if (A / 2), (B / 2) and (C / 2) are in Arithmetic progression, then which of the following option is always correct?

Options

  1. Acos A, cosB and cosC are in Arithmetic Progression.
  2. Bcos A, cosB and cosC are in Geometric Progression.
  3. Ccos A, cosB and cosC are in harmonic Progression.
  4. Dno conclusion can be made with given data.

Correct answer

A. cos A, cosB and cosC are in Arithmetic Progression.

Step-by-step solution

Given In a A B C, (A / 2), (B / 2), (C / 2) are in Arithmetic progression, aligned & (B / 2)- (A / 2)= (C / 2)- (B / 2) & (B / 2) (B / 2) - (A / 2) (A / 2) & = (C / 2) (C / 2) - (B / 2) (B / 2) & (B / 2) (A / 2)- (A / 2) (B / 2) (B / 2) (A / 2) & = (C / 2) (B / 2)- (B / 2) (C / 2) (C / 2) (B / 2) & ( B 2 - A 2 ) (A / 2) = ( C 2 - B 2 ) (C / 2) ...(i) aligned . A+B+C=180^ (angle sum property in A B C ) gathered A 2 = 1 2 180-(B+C) A 2 =90- ( B 2 + C 2 ) and C 2 =90- ( A 2 + B 2 ) gathered From Eq. (i), we get aligne

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