Question

已知cos(x-兀/4)=√2/10 x∈(兀/2,3兀/4)求sinx

Answer 1

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