已知cos(x-兀/4)=√2/10,x属于（兀/2,3兀/4) 求sinx的值,求sin(2x+兀/3)的值

cos(x-兀/4)=cos x cos (兀/4)+sin x sin (兀/4)=√2/2 [cos x +sin x]=√2/10
所以 cos x +sin x =1/5 又 cos^2 x +sin^2 x = 1
所以 (1/5 - sin x)^2 + sin^2 x = 1,所以 2sin^2 x - 2/5 sin x - 24/25 = 0
所以 sin x = - 4/5 (x属于（兀/2,3兀/4),sin x