abc成等差数列,B=π/4,A+C=3π/4
sinA,sinB,sinC成等差数列,sinB=√2/4,sinA+sinC=2sinB=√2
(sinA+sinC)^2=2
设cosA-cosC=t
t^2=(cosA-cosC)^2
(cosA-cosC)^2+(sinA+sinC)^2=t^2+2
sinA * sinA+cosA * cosA=1;
sinC * sinC+cosC * cosC=1;
2sinA * sinC - 2cosA * cosC + 2 = t^2+2
2sinA * sinC - 2cosA * cosC=t^2
- 2cos(A+C)=-2cos3π/4=√2=t^2
t=±2^(1/4)=cosA-cosC