lim（x趋于π/2)（tanx/tan3x）求极限过程是这样子的limtanx/tan3x=lim(1/cosx^2)/(3/cos3x^2)=lim(cos3x^2)/3cosx^2=lim6cos3x(-sin3x)/6cosx(-sinx)=limsin6x/sin2x=lim6cos6x/2cos2x=-6/-2=3我想问的是=lim(cos3x^2)/3cosx

Question

lim（x趋于π/2)（tanx/tan3x）求极限
过程是这样子的
lim tanx/tan3x
=lim ( 1/cosx^2) / (3/cos3x^2)
= lim (cos3x^2)/3cosx^2
= lim 6cos3x(-sin3x)/6cosx(-sinx)
= lim sin6x/sin2x
= lim 6cos6x/2cos2x
= -6 / -2 = 3
我想问的是= lim (cos3x^2)/3cosx^2
= lim 6cos3x(-sin3x)/6cosx(-sinx)
= lim sin6x/sin2x
这里是怎么得到的

Answer 1

二倍角公式,2sinxcosx=sin2x