求函数y=[sin2x+sin(2x+π/3)]/[cos2x +cos(2x+π/3)]的最小正周期

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求函数y=[sin2x+sin(2x+π/3)]/[cos2x+cos(2x+π/3)]的最小正周期求函数y=[sin2x+sin(2x+π/3)]/[cos2x+cos(2x+π/3)]的最小正周期

求函数y=[sin2x+sin(2x+π/3)]/[cos2x +cos(2x+π/3)]的最小正周期
求函数y=[sin2x+sin(2x+π/3)]/[cos2x +cos(2x+π/3)]的最小正周期

求函数y=[sin2x+sin(2x+π/3)]/[cos2x +cos(2x+π/3)]的最小正周期
sin(2x+π/3)=1/2*sin2x+√3/2*cos2x
所以sin2x+sin(2x+π/3)=3/2*sin2x+√3/2*cos2x
=√3(√3/2*sin2x+1/2*cos2x)
=√3sin(2x+π/6)
同理cos2x +cos(2x+π/3)=√3cos(2x+π/6)
所以y=sin(2x+π/6)/cos(2x+π/6)=tg(2x+π/6)
最小正周期T=π/w=π/2

化简。y=-sin(2x+π/6)/sin(2x-π/3)
所以 T=π