当x趋向90度时sinx^tgx的极限！大哥们不要用罗必塔法则 谢谢！

(sinx)^tanx = (1 + sinx - 1)^tanx

= (1 + sinx - 1)^[tanx(sinx - 1)/(sinx - 1)]

= {(1 + sinx - 1)^[1/(sinx - 1)]}^[tanx(sinx - 1)]

u = x - 90度
x = u + 90度

tanx(sinx - 1) = tan(u + 90度)[sin(u + 90度) - 1]

= -cot(u)[cosu-1]

= cosu[1 - cosu]/sinu

= 2(cosu)[sin(u/2)]^2/[2sin(u/2)cos(u/2)]

= (cosu)tan(u/2)

x趋向90度时
(1 + sinx - 1)^[1/(sinx - 1)] 趋向于 e,

u 趋向于 0，
tanx(sinx - 1) = (cosu)tan(u/2)趋向于 0，

所以，
原极限 = e^0 = 1