题目

求等差、等比数列的前n项和公式,以及三角涵数常用的变换公式
另外再问问,secx=1/cosx,cscx=1/sinx是否正确?太久不用记不清了,

提问时间：2020-07-25

答案

等差：Sn=n(a1+an)/2,Sn=na1+n(n-1)d/2
等比：Sn=a1(1-q^n)/(1-q),Sn=(a1-anq)/(1-q)注意q不=1
三角：
1.基本关系：(sinx)^2+(cosx)^2=1,tanx=sinx/cosx,secx=1/cosx,cscx=1/sinx,(secx)^2=1+(tanx)^2,(cscx)^2=1+(cotx)^2
2.二倍交公式：sin2x=2sinx*cosx,变形：sinx*cosx=sin2x/2
1+sinx=(sin(x/2))^2+(cos(x/2))^2+2sin(x/2)cos(x/2)=[sin(x/2)+sin(x/2)]^2
1-sinx=(sin(x/2))^2+(cos(x/2))^2-2sin(x/2)cos(x/2)=[sin(x/2)-sin(x/2)]^2
cos2x=(cosx)^2-(sinx)^2
=2(cosx)^2-1,变形：(cosx)^2=(1+cos2x)/2
=1-2(sinx)^2,变形：(sinx)^2=(1-cos2x)/2
tan2x=2tanx/(1-(tanx)^2)
3.两角和与差公式：sin(x+y)=sinxcosy+sinycosx,sin(x-y)=sinxcosy-sinycosx
cos(x+y)=cosxcosy-sinxsiny,cos(x-y)=cosxcosy+sinxsiny
tan(x+y)=(tanx+tany)/(1-tanxtany),变形：tanx+tany=tan(x+y)(1-tanxtany)
tan(x-y)=(tanx-tany)/(1+tanxtany),变形：tanx-tany=tan(x-y)(1+tanxtany)
4.万能公式：sin2x=2tanx/(1+(tanx)^2),
cos2x=(1-(tanx)^2)/(1+(tanx)^2)