已知cos(x-派/4)=根2/10,x属于(派/2,3派/4),求cos(2x+派/3)的值

已知cos(x-派/4)=根2/10,x属于(派/2,3派/4),求cos(2x+派/3)的值
已知cos(x-派/4)=根2/10,x属于(派/2,3派/4),求cos(2x+派/3)的值

已知cos(x-派/4)=根2/10,x属于(派/2,3派/4),求cos(2x+派/3)的值
已知,cos(x-π/4)=√2/10,x属于(π/2,3π/4),求cos(2x+π/3)的值
cos(x-π/4)=√2/2(cosx+sinx)=√2/10 ,sinx+cosx=1/5 ,1+sin2x=1/25,sin2x=-24/25 ,cos2x=-7/25
cos(2x+π/3)=1/2cos2x-√3/2sin2x=(-7/50)+24√3/50=(24√3-7)/50

∵cos(x-π/4)=√2/10∴cosx+sinx=1/5∴sin2x=-24/25∵x∈[π/2,3π/4]∴2x∈[π,3π/2]∴cos2x=-7/25
∴cos(2x+π/3)=(1/2)cos2x-(√3/2)sin2x=(24√3-7)/50