b,
Thay
b² - c² = a² - 2ca.cosB = a(a - 2c.cosB);
c² - a² = b² - 2ab.cosC = b(b - 2a.cosC);
a² - b² = c² - 2bc.cosA = c(c - 2b.cosA);
bc(b² - c²)cosA + ca(c² - a²)cosB + ab(a² - b²)cosC = 0 (1)
<=> abc(a - 2c.cosB)cosA + abc(b - 2a.cosC)cosB + abc(c - 2b.cosA)cosC = 0
<=> a.cosA + b.cosB + c.cosC - 2c.cosA.cosB - 2a.cosB.cosC - 2b.cosC.cosA = 0
<=> a.cosA + b.cosB + c.cosC - c[cos(A + B) + cos(A - B)] - a[cos(B + C) + cos(B - C)] - b[cos(C + A) + cos(C - A) = 0
<=> a.cosA + b.cosB + c.cosC - c[- cosC + cos(A - B)] - a[- cosA + cos(B - C)] - b[ - cosB + cos(C - A) = 0
<=> 2(a.cosA + b.cosB + c.cosC) - c.cos(A - B) - a.cos(B - C) - b.cos(C - A) = 0
<=> 2R(2sinA.cosA + 2sinB.cosB + 2sinC.cosC) - 2RsinC.cos(A - B) - 2RsinA.cos(B - C) - 2RsinB.cos(C - A) = 0
<=> sin2A + sin2B + sin2C - sin(A + B).cos(A - B) - sin(B + C).cos(B - C) - sin(C + A).cos(C - A) = 0
<=> sin2A + sin2B + sin2C - (1/2)(sin2A + sin2B) - (1/2)(sin2B + sin2C) - (1/2)(sin2C + sin2A) = 0 (2)
(2) đúng nên (1) đúng