求y=lim（x→（π/4））（（sinx-cos - 知识问答

求y=lim（x→（π/4））（（sinx-cosx）/（1-（（tanx）^2）））的值

2个回答

(sinx-cosx)/(1-tan^2x)
=(sinx-cosx)/[(cos^2x-sin^2x)/cos^2x]
=-cos^2x/(cosx+sinx)
lim(x→π/4) (sinx-cosx)/(1-tan^2x)
=lim(x→π/4) -cos^2x/(cosx+sinx)
=-cos^2(π/4)/(cosπ/4+sinπ/4)
=-(√2/2)^2/(√2/2+√2/2)
=-√2/4

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