x趨近三分之派的sin(x-三分之派)比上1-2cosx的極限

x趨近三分之派的sin(x-三分之派)比上1-2cosx的極限

原式=lim(x->π/3)[cos(x-π/3)/(2sinx)] (0/0型極限,應用羅比達法則)
=cos(π/3-π/3)/(2sin(π/3))
=1/(2*(√3/2))
=√3/3.