lim(x→π/4) tan(π/4-x)/cot2x 求极限
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lim(x→π/4) tan(π/4-x)/cot2x 求极限
lim(x→π/4) tan(π/4-x)/cot2x 求极限
lim(x→π/4) tan(π/4-x)/cot2x 求极限
令a=π/4-x
则a→0
cot2x=tan(π/2-2x)=tan2a=2tana/(1-tan²a)
所以原式=lim(a→0)tana/[2tana/(1-tan²a)]
=lim(a→0)(1-tan²a)/2
=(1-0)/2
=1/2
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