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find the range of function f(x)=sin(x+(p...

find the range of function `f(x)=sin(x+(pi)/(6))+cos(x-(pi)/(6))`

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`f(x)=sin(x+(pi)/(6))+cos(x-(x)/(6))`
`=sin x cos(pi)/(6)+cos x sin(pi)/(6)+cos x cos (pi)/(6)+sin x sin(pi)/(6)`
`=(sqrt(3)+1)/(2) (sin x+cos x)`
Now, `sin x+cos x in [-sqrt(2),sqrt(2)]`
`therefore f(x)=(sqrt(3)+1)/(2)(sin x+cos x)in[-sqrt(2)xx(sqrt(3)+1)/(2),sqrt(2)xx(sqrt(3)+1)/(2)]`
or `f(x)in[-(sqrt(3)+1)/(sqrt(2)),(sqrt(3)+1)/sqrt(2)]`
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