(2c-a)/b=(2sinC-sinA)/sinB
So (COSA-2 COSC)SINB =(2 SINC- Sina) COSB.
B=π-(A+C)
sinB=sin(A+C),cosB=-cos(A+C)
Then (COSA-2 COSC) SIN (A+C) =-COS (A+C) (2 SINC-Sina)
Simplified to sinC-2sinA=0.
So sinC/sinA=2
I hope it helps you. . .