∴cosa= 1/2==>； A=π/3

∵b= 1,∴a^2=c^2-c+ 1

∫tan(A-C)=√3/3 = = & gt； A-C=π/6== >C=π/6

∴B=π/2,c= 1/2

(2) Analysis: Let a=2c.

∵a^2=b^2+c^2-bc==>； 3c^2+bc-b^2=0==>； 3c^2+c- 1=0==>； c=(√ 13- 1)/6

s = 1/2 bcsina = 1/2 *(ì 13- 1)/6 *√3/2 =√3(√ 13- 1)/24