已知cos(π-x)=3/5,x∈[0,π),则sin(2x-π/4)=

问题描述:

已知cos(π-x)=3/5,x∈[0,π),则sin(2x-π/4)=

∵cos(π-x)=3/5
∴cosx=-3/5
sinx=4/5
∴sin2x=2sinx*cosx=-24/25
cos2x=(cosx)平方-(sinx)平方=-7/25
∵sin(2x-π/4)
=sin2xcosπ/4-cos2xsinπ/4
=根号2/2*sin2x-根号2/2*cos2x
=根号2/2(sin2x-cos2x)
=-17根号2/50