f(x)＝3sin(x+π/9)＋5sin(x＋4π/9)
=3sinxcos(π/9)+3cosxsin(π/9)+5sinxcos(4π/9)+5cosxsin(4π/9)
=[3cos(π/9)+5cos(4π/9)]sinx+[3sin(π/9)+5sin(4π/9)]cosx
=√[3cos(π/9)+5cos(4π/9)]²+[3sin(π/9)+5sin(4π/9)]²sin(x+φ)
∴最大值=√[3cos(π/9)+5cos(4π/9)]²+[3sin(π/9)+5sin(4π/9)]²
=7
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