cos(a-π/4)=1/4,则sin2a

问题描述:

cos(a-π/4)=1/4,则sin2a

cos(a-π/4)=cosacosπ/4+sinasinπ/4=√2/2cosa+√2/2sina=√2/2(cosa+sina)=1/4sina+cosa=√2/4sin2a=2sinacosa=(sina+cosa)²-(sin²a+cos²a)=1/8-1=-7/8