已知向量a=(sinx,2),b=(cosx,1),且a//b,其中x属于（0,90） 求 sinx 和cos x的值

a//b
=>sinx/2 = cosx/1
tanx=1/2
sinx = √5/5
cosx = 2√5/5
sin(x-w) = 3/5
=> x-w 属于（0,90）
sin(x-w) = 3/5
sinxcosw-cosxsinw = 3/5
(√5/5cosw)- (2√5/5)sinw = 3/5
[(√5/5cosw)- 3/5]^2= [(2√5/5)sinw]^2
(1/5)(cosw)^2 - (6√5/25)cosw + 9/25 = 4/5( 1- (cosw)^2)
5(cosw)^2 - 6√5cosw +9 = 20(1-(cosw)^2 )
25(cosw)^2- 6√5cosw -11 =0
cosw = (6√5+16√5) /50 or (6√5-16√5) /50 ( rejected)
= 11√5/25