1-cosx = 1-{1-2[sin(x/2)]^2} = 2[sin(x/2)]^2xsinx = 2xsin(x/2)cos(x/2)原式= lim 2[sin(x/2)]^2 / [2xsin(x/2)cos(x/2)] = tgx / x对分子分母同时求导(洛必达法则)(tgx)' = 1 / (cosx)^2(x)' = 1原式 = lim 1/(cosx)^2 当 x --> 0 时,cosx ---> 1原式 = 1