已知函数f(x)=sin(x-π/6)+sin(x-π/6)+cosx+a(a属于R,a是常数))（2）若x属于[-π/2,π/2]时,f(x)的最大值为1,求a的值.

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已知函数f(x)=sin(x-π/6)+sin(x-π/6)+cosx+a(a属于R,a是常数))（2）若x属于[-π/2,π/2]时,f(x)的最大值为1,求a的值.
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已知函数f(x)=sin(x-π/6)+sin(x-π/6)+cosx+a(a属于R,a是常数))（2）若x属于[-π/2,π/2]时,f(x)的最大值为1,求a的值.
已知函数f(x)=sin(x-π/6)+sin(x-π/6)+cosx+a(a属于R,a是常数)
)（2）若x属于[-π/2,π/2]时,f(x)的最大值为1,求a的值.

已知函数f(x)=sin(x-π/6)+sin(x-π/6)+cosx+a(a属于R,a是常数))（2）若x属于[-π/2,π/2]时,f(x)的最大值为1,求a的值.
f(x)=sinxcosπ/6-cosxsinπ/6+sinxcosπ/6+cosxsinπ/6+cosx+a
=2sinxcosπ/6+cosx+a
=√3sinx+cosx+a
=2sin(x+π/6)+a
f(x)=2sin(x+π/6)+a
-π/2

f(x)=sinxcosπ/6-cosxsinπ/6+sinxcosπ/6+cosxsinπ/6+cosx+a.
=2sinxcosπ/6+cosx+a.
=√3sinx+cosx+a.
=2sin(x+π/6)+a.
则f(x)=2sin(x+π/6)+a.
又因为-π/2-π/3x+π/6=π/2，f(x)最大=2sin(π/2)+a=2+a.
所以2+a =1.
即a=-1.

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