求极限：lim tan2x·tan(π/4-x)（x趋于π/4） 越详细越好,最好有每一步的步骤
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lim(x→π/4) tan2x*tan(π/4-x)
=lim(x→π/4) 2tanx/(1-tan^2x)*[tan(π/4)-tan(x)]/[1+tan(π/4)*tan(x)]
=lim(x→π/4) 2tanx/(1-tan^2x)*[1-tan(x)]/[1+tan(x)]
=lim(x→π/4) 2tanx/(1+tanx)^2
=2tanπ/4/(1+tanπ/4)^2
=2/(1+1)^2
=2/4
=1/2
=lim(x→π/4) 2tanx/(1-tan^2x)*[tan(π/4)-tan(x)]/[1+tan(π/4)*tan(x)]
=lim(x→π/4) 2tanx/(1-tan^2x)*[1-tan(x)]/[1+tan(x)]
=lim(x→π/4) 2tanx/(1+tanx)^2
=2tanπ/4/(1+tanπ/4)^2
=2/(1+1)^2
=2/4
=1/2
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