cos(x-pai/4)=根号2/10,x属于(pai/2,3pai/4)求sinx和sin(2x+pai/3)

cos(x-π/4)
=cosxcosπ/4+sinxsinπ/4
=√2/2*(cosx+sinx)=√2/10
sinx+cosx=1/5
cosx=1/5-sinx
平方
cos²x=1-sin²x=1/25-2/5*sinx+sin²x
sin²x-1/5*sinx-12/25=0
(sinx-4/5)(sinx+3/5)=0
由x范围
sinx>0
sinx=4/5
cosx=1/5-sinx=-3/5
sin2x=2sinxcosx=-24/25
cos2x=cos²x-sin²x=-7/25
sin(2x+π/3)
=sin2xcosπ/3+cos2xsinπ/3
=-(24+7√3)/50