Question

求函数y=cosx+cos(x-π/3)的最大值

过程稍微详细

Answer 1

解答：
y=cosx+cos(x-π/3)
=cosx+cosxcos(π/3)+sinxsin(π/3)
=(3/2)cosx+(√3/2)sinx
=√3* [cosx*(√3/2)+sinx*(1/2)]
=√3[cosxsin(π/3)+cosxsin(π/3)]
=√3sin(x+π/3)
所以函数y=cosx+cos(x-π/3)的最大值为√3

Answer 2

解

y=cosx+cos(x-π/3)
=2cos[(x+x-π/3)/2]·cos[(x-(x-π/3))/2]
=2cos（x-π/6）cosπ/6
=√3cos（x-π/6）

函数y=cosx+cos(x-π/3)的最大值为√3

（这是基于和差化积公式cos α+cos β=2cos[(α+β)/2]·cos[(α-β)/2] ）

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