f(π/3)=Acos(π/12+π/6)=Acos(π/4)=A*√2/2=√2
所以A=2
(2)
f(x)=2cos(x/4+π/6)
根据题意得
-30/17=2cos[(4α+4π/3)/4+π/6]
=2cos(α+π/3+π/6)
=2cos(π/2+α)
=-2sinα
∴sinα=15/17
同理
8/5=2cos[(4β-2π/3)/4+π/6]=2cos(β-2π/12+2π/12)=2cosβ
∴cosβ=4/5
∵α,β∈[0,π/2]
∴cosα=√(1-sin²a)=√[1-(15/17)²]=8/17
sinβ=√(1-cos²β)=√[1-(4/5)²]=3/5
∴cos(α+β)=cosαcosβ-sinαsinβ
=8/17*(4/5)-15/17*(3/5)
=32/85-45/85
=-13/85