Question

请写出详细的解题步骤，谢谢

Answer 1

19
(1)∵函数f(x)=Asin(x+φ)(a>0,0<φ<π)x∈R的最大值是1
∴A=1
∴f(x)=sin(x+φ)
x+φ=2kπ+π/2=x=2kπ+(π-2φ)/2
∵其图像经过点M(π/3,1/2)
π/3+φ=π/6==>φ=-π/6，π/3+φ=5π/6==>φ=π/2
∵0<φ<π
∴f(x)=sin(x+π/2)
(2)
∵α，β∈（0，π/2），且f（α）=3/5，f（β）＝12/13，
f(α)=sin(α+π/2)=3/5 cosα=3/5 sinα=4/5
f(β)=sin(β+π/2)=12/13 cosβ=12/13 sinβ=5/13
f(α-β)=sin(α-β+π/2)=cos(α-β)=cosαcosβ+sinαsinβ
=36/65+20/65=56/65