已知函数f(x)=sin(x+π/6)+2sin∧2 x/2,求f(x)最大值

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已知函数f(x)=sin(x+π/6)+2sin∧2 x/2,求f(x)最大值

已知函数f(x)=sin(x+π/6)+2sin∧2 x/2,求f(x)最大值
已知函数f(x)=sin(x+π/6)+2sin∧2 x/2,求f(x)最大值

已知函数f(x)=sin(x+π/6)+2sin∧2 x/2,求f(x)最大值
f(x)=sin(x+π/6)+2sin∧2 x/2
=sin(x+π/6)+1-cosx
=sinxcos(π/6)+cosxsin(π/6)+1-2cosxsin(π/6)
=sinxcos(π/6)-cosxsin(π/6)+1
=sin(x-π/6)+1
-2≤f(x)≤2
f(x)最大值是2