由余弦定理知
C²=a²﹢b²﹣2abcosC
=1﹢4-2×2×1/4=4
C=2
∵cosC=1/4
∴sinC=√15/4
由正弦定理知
a/sinA=c/sinC
即1/sinA=2/﹙√15/4﹚
sinA=√15/8
cosA=7/8
∴cos(A-C)=cosAcosC﹢sinAsinC
=7/8×1/4﹢√15/8×√15/4
=11/16
由余弦定理知
C²=a²﹢b²﹣2abcosC
=1﹢4-2×2×1/4=4
C=2
∵cosC=1/4
∴sinC=√15/4
由正弦定理知
a/sinA=c/sinC
即1/sinA=2/﹙√15/4﹚
sinA=√15/8
cosA=7/8
∴cos(A-C)=cosAcosC﹢sinAsinC
=7/8×1/4﹢√15/8×√15/4
=11/16