数学问答二解答问题g
2010-06-02 15:05:54l***
数学问答二解答问题 g数学问答二解答问题g:设an=arccot(2n^2),
则tan(an)=1/(2n^2),
∴tana1=1/2,
tan(a1+a2)=[1/2+1?
最佳回答
设an=arccot(2n^2),
则tan(an)=1/(2n^2),
∴tana1=1/2,
tan(a1+a2)=[1/2+1/8]/[1-1/2*1/8]=10/15=2/3.
假设tan(Sn)=n/(n+1),那么
tan(S)=tan(Sn+a)
={n/(n+1)+1/[2(n+1)^2]}/{1-n/(n+1)*1/[2(n+1)^2]}
=(n+1)[2n(n+1)+1]/[2(n+1)^3-n]
=(n+1)/(n+2).
∴对于任意的n∈N+,都有tan(Sn)=n/(n+1)<1,
易知Sn为锐角,故Sn<π/4.
2010-06-02 16:50:37
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