y=sin2xcos2x的最小正周期是?y=sin2xcos2x=1/2sin4xT=2π/w=2π/4=π/2但是看不懂~y=sin2xcos2x=1/2sin4x怎么变得?

Question

y=sin2xcos2x的最小正周期是?
y=sin2xcos2x=1/2sin4x T=2π/w=2π/4=π/2
但是看不懂~y=sin2xcos2x=1/2sin4x 怎么变得?

Answer 1

这是二倍角公式
sin(2x)=2sinx·cosx
sin(2x)
=sin(x+x)
=sinx·cosx+cosx·sinx
=2sinx·cosx
题中y=sin(2x)·cos(2x)=1/2[2sin(2x)·cos(2x)]=1/2sin(4x)
T=2π/w=2π/4=π/2