已知函数f(x)=cos²(x+π/12)+1/2sin2x
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f(x)=cos^2(x+π/12)+1/2sin2x
=[cos(2x+π/6)+1]/2+1/2sin2x
=√3/4cos2x+1/4sin2x
=1/2(√3/2*cos2x+1/2*sin2x)
=1/2sin(2x+π/3)
(1)f(x)的最大值=1/2；最小值=-1/2
(2)当2kπ-π/2<=2x+π/3<=2kπ+π/2
即kπ-5π/12<=x<=kπ+π/12
为函数增区间
当2kπ+π/2<=2x+π/3<=2kπ+3π/2即kπ+π/12<=x<=kπ+7π/12
为函数减区间
=[cos(2x+π/6)+1]/2+1/2sin2x
=√3/4cos2x+1/4sin2x
=1/2(√3/2*cos2x+1/2*sin2x)
=1/2sin(2x+π/3)
(1)f(x)的最大值=1/2；最小值=-1/2
(2)当2kπ-π/2<=2x+π/3<=2kπ+π/2
即kπ-5π/12<=x<=kπ+π/12
为函数增区间
当2kπ+π/2<=2x+π/3<=2kπ+3π/2即kπ+π/12<=x<=kπ+7π/12
为函数减区间
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