lim x趋于0 1-cosx^2/x^2sinX^2(1-cosx^2)/x^2sinx^2=[1-1-2sin^2(x^2/2)]/x^2sinx^2=2sin^2(x^2/2)/x^2sinx^2=(x->0)2(x^2/2)^2/x^2*x^2=1/2第二步是怎么来的?(1-cosx^2)/x^2sinx^2①=[1-1-2sin^2(x^2/2)]/x^2sinx^2②=2sin^2(x^2/2)/x^2sinx^2③=(x->0)2

Question

lim x趋于0 1-cosx^2/x^2sinX^2
(1-cosx^2)/x^2sinx^2
=[1-1-2sin^2(x^2/2)]/x^2sinx^2
=2sin^2(x^2/2)/x^2sinx^2
=(x->0)2(x^2/2)^2/x^2*x^2=1/2
第二步是怎么来的?
(1-cosx^2)/x^2sinx^2①
=[1-1-2sin^2(x^2/2)]/x^2sinx^2②
=2sin^2(x^2/2)/x^2sinx^2③
=(x->0)2(x^2/2)^2/x^2*x^2=1/2④

Answer 1

高中的公式：cos2A=1-2(sinA)^2.
令A=(x^2)/2,代入得:cosx^2=1-2sin^2(x^2/2).
因此,第2步的第二个减号应改为加号.