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MHT CET202617 April 2026Evening ShiftMathematicsProperties of TrianglesActual

In ABC , with usual notation, if cot A, cot B, cot C are in arithmetic progression, then

Options

  1. Asin A, sin B, sin C are in arithmetic progression.
  2. Ba^2, b^2, c^2 are in arithmetic progression.
  3. Ccos A, cos B, cos C are in arithmetic progression.
  4. Da, b, c are in arithmetic progression.

Correct answer

B. a^2, b^2, c^2 are in arithmetic progression.

Step-by-step solution

Given A, B, C are in A.P. We know that A = A A . Using the cosine rule, A = b^2 + c^2 - a^2 2bc and using the sine rule, A = a 2R . Therefore, A = b^2 + c^2 - a^2 2bc 2R a = R(b^2 + c^2 - a^2) abc . Similarly, B = R(c^2 + a^2 - b^2) abc and C = R(a^2 + b^2 - c^2) abc . Since A, B, C are in A.P., we have: 2 B = A + C Substituting the expressions, we get: 2 ( R(c^2 + a^2 - b^2) abc ) = R(b^2 + c^2 - a^2) abc + R(a^2 + b^2 - c^2) abc Cancelling the common term R abc from both sides: 2(c^2 + a^2 - b^2) = (b^2 + c^2 - a

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