f(x)=2sinx*sin2X
=2sinx*2sinx*cosx
=4(1-cosx^2)cosx
=4(cosx-cosx^3)
令cosx=t,-1≤t≤1
f(x)=4(t-t^3)
然后求导求最值即可
f'(x)=4(1-3t^2)=0
t=±√3/3
f(x)max=8√3 /9