y=sin(x+π /6）sin(x-π/6）的最小周期是

题目

y=sin(x+π /6）sin(x-π/6）的最小周期是

答案

积化和差
y=sin(x+π/6)sin(x-π/6)
=[cos(x+π/6-x+π/6)-cos(x+π/6+x-π/6)]/2
=[cos(π/3)-cos(2x)]/2
=1/4-cos2x/2
故T=2π/2=π
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