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

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

已知cos(x-派/4)=根号2/10,x属于(派/2,3派/4)求sinx的值
cos2(x-派/4)=2cos(x-派/4)^2-1=-24/25=cos(2x-π/2)=-sin2x
所以 sin2x=24/25=2sinx*cosx cos2x=-7/25 =1-2sinx^2
sinx>0 得sinx=4/5

sinX=4/5