若cos2α/sin(α+π/4)=1/2,则sin2α的值为

问题描述:

若cos2α/sin(α+π/4)=1/2,则sin2α的值为

(cos^2a-sin^2a)/[1/√2*(sina+cosa)]=1/2
cosa-sina=1/2√2
cos^2a-2sinacosa+sin^2a=1/8
sin2a=1-1/8=7/8[1/√2*(sina+cosa)]这一步怎么得来的sin(a+π/4)=sinacosπ/4+cosasinπ/4=1/√2*(sina+cosa)还是不懂