(tanX-sinX) X^2*sinX

lim(x→0)[(tanx-sinx)/(sin^22x)]=lim(x→0)[tanx(1-cosx)/(2x)^2]=lim(x→0)[x*x^2/2]/(2x)^2=0

lim(sinx)^tanx=lime^[tanx*lnsinx]=e^{lim[lnsinx/cotx]}利用洛必达法则=e^{lim[(cosx/sinx)/(-1/(sinx)^2)]}=e^{

先等价无穷小代换：lim（x→0）(tanx-sinx)/xsinx^2=lim（x→0）(tanx-sinx)/x^3原式=lim(sin/cosx-sinx)/x³=limsinx(1-

解法一：∵lim(x->π/2)[(sinx-1)tanx]=lim(x->π/2){[(sinx-1)/cosx]sinx}=lim(x->π/2)[(sinx-1)/cosx]*lim(x->π/

sinx=2sinx/2cosx/2=2[cos(x/2)]^2(tgx/2)=2tg(x/2)/[1+[tg(x/2)]^2]cosx=2(cosx/2)^2-1=2/[1+(tg(x/2)^2]-

(sinx+cosx)/(sinx-cosx)=3sinx+cosx=3sinx-3cosxsinx=2cosxtanx=sinx/cosx=2sinx=2cosx带入恒等式sin²x+co

注：设0

(sinx+tanx)/(cos^2x+sin^2x+cosx)=(sinx+sinx/cosx)/(1+cosx)=sinx(cosx+1)/[cosx(1+cosx)]=sinx/cosx=tan

tan(3x/2)-tan(x/2)=[sin(3x/2)/cos(3x/2)-sin(x/2)/cos(x/2)]=(sin3x/2cosx/2-con3x/2sinx/2)/cos3x/2cosx

lim(x趋向于0)((tanx-sinx)/(x*(sinx)^2))=lim(x趋向于0)[(sinx/cosx-sinx)]/x(sinx)^2=lim(x趋向于0)[1-cosx)/x(sin

(sinx)^2tanx=[1-(cosx)^2]tanx=tanx-(cosx)^2tanx=tanx-(cosx)^2*sinx/cosx=tanx-sinxcosx(cosx)^2cotx=[1

如果你没有抄错.x→0时,2+x→2,(2+x)^2→4,(2+x)^2\4→1sinx→0,2+sinx→2,(2+sinx)^1\2-1→根号2-1分子→0-0=0分母不是无穷小,则极限为0.再问

(sinx)^2tanx=[1-(cosx)^2]tanx=tanx-(cosx)^2tanx=tanx-(cosx)^2*sinx/cosx=tanx-sinxcosx(cosx)^2cotx=[1

这里用到:(sin)^2+(cosx)^2=1,原式=(cosx-sinx)^2/(cosx+sinx)(cosx-sinx)=(cosx-sinx)/(cosx+sinx)=(1-tanx)/(1+

右式=(cos²x-sin²x)/sinx*cosx=cosx/sinx-sinx/cosx=1/tanx-tanx=左式

2x不是角度,是弧度,弧度为实数,在这个大前提下：令F(x)=sinx+tanx-2x,对其求导得cosx+sec^2x-2,即cos+1/cos^2x-2,实行平均值不等式,有1/2cosx+1/2

大神sinx/tanx=cosx(sinx/tanx-6x+x^2)/sinx=cosx/sinx+(-6x+x^2)/sinx=无穷大吧在里面也不能换

希望没有白干活啊

lim(tanx-sinx)/(x^2*sinx)=limtanx(1-cosx)/(x^2*sinx)(等价无穷小代换)=limx(x^2/2)/(x^2*x)=1/2