x趋近于0 lim 1/x(1/sinx-1/tanx)

问题描述:

x趋近于0 lim 1/x(1/sinx-1/tanx)

我去没法写1/2

原式=lim(x→0)(sinx/cosx-sinx)/(xsinxtanx)
=lim(x→0)(1-cosx)/(xtanx)*1/cosx
=lim(x→0)2sin^2(x/2)/(xtanx)
=lim(x→0)2*(x/2)^2/x^2 (x~sinx~tanx)
=1/2