已知向量α＝(cosx,sinx),b＝(√2,√2),a·b＝8/5则tan(x－π／4)的值为

ab=√2cosx+√2sinx=8/5得sinx+cosx=(4/5)√2于是(sinx+cosx)^2=32/25即1+2sinxcosx=32/25,得2sinxcosx=7/25那么(sinx-cosx)^2=1-2sinxcosx=1-7/25=18/25得sinx-cosx=±(3/5)√2tan(x-π/4)=(tanx-1)/(tanx+1)=(sinx-cosx)/(sinx+cosx)=[±(3/5)√2]/[(4/5)√2]=±3/4