已知 f(x)=sin(2x+π/6)+cos(2x-π/3) ,求f(x)的最大值及取得最大值时X的值.

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已知 f(x)=sin(2x+π/6)+cos(2x-π/3) ,求f(x)的最大值及取得最大值时X的值.
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已知 f(x)=sin(2x+π/6)+cos(2x-π/3) ,求f(x)的最大值及取得最大值时X的值.
已知 f(x)=sin(2x+π/6)+cos(2x-π/3) ,求f(x)的最大值及取得最大值时X的值.

已知 f(x)=sin(2x+π/6)+cos(2x-π/3) ,求f(x)的最大值及取得最大值时X的值.
f(x)=sin(2x+π/6)+cos(2x-π/3)
=sin(2x)cos(π/6)+cos(2x)sin(π/6)+cos(2x)cos(π/3)+sin(2x)sin(π/3)
=sin(2x)[cos(π/6)+sin(π/3)]+cos(2x)[sin(π/6)+cos(π/3)]
=2sin(2x)cos(π/6)+2cos(2x)sin(π/6)
=2sin(2x+π/6)

cos(2x-π/3)=cos(π/3-2x)=sin(2x+π/6)所以原式=2sin(2x+π/6)