问一个三角函数求极限的问题?求：(sin x - cos x) / (tan x - 1) 当x趋向于 Pi/4 时的极限,请写出步骤,
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运用洛必达法则,上下求导就可以了啊
lim(x→π/4)(sin x - cos x) / (tan x - 1)
=lim(x→π/4)(sin x +cos x) / sec ^2x
=lim(x→π/4)(sin x +cos x)*cos ^2x
=√2*(√2/2)^2
=√2/2======以下答案可供参考======
供参考答案1:
lim(sin x - cos x) / (tan x - 1) (洛必达法则)
=lim(cosx+sinx)/(secx)^2
=( √2/2+√2/2)/(1/√2/2)^2
=√2/2.
供参考答案2:
求导（cosx+sinx）*cos^2x
=(根号2)/2