Question

急！！！一道高一数学填空题

希望能够写出过程
(1-tanx)/(1+tanx)=2010,则sin2x+cos2x=

Answer 1

sin2x+cos2x
=2sinxcosx+(cosx)^2-1
=2sinxcosx+(cosx)^2-[(sinx)^2+(cosx)^2]
=[2sinxcosx-(sinx)^2]/1............1=(sinx)^2+(cosx)^2
=[2sinxcosx-(sinx)^2]/[(sinx)^2+(cosx)^2].....tanx=sinx/cosx
等号两边同时除以(cosx)^2
=[2tanx-(tanx)^2]/[(tanx)^2+1]

又因为(1-tanx)/(1+tanx)=2010
(1-tanx+tanx-tanx)/(1+tanx)=2010
[(1+tanx)-2tanx]/(1+tanx)=2010
1-2tanx/(1+tanx)=2010
2tanx/(1+tanx)=-2009
(2tanx+2-2)/(1+tanx)=-2009
2-2/(1+tanx)=-2009
tanx=-2009/2011

代入sin2x+cos2x=4044117/8080202~~0.50049

Answer 2

1-(tanx )^2 = 2010
2-[1+(tanx)^2] =2010
1/(cosx)^2=2008
2/(cos2x+1)=2008
cos2x = [根号(1/1004)]-1
sin2x+cos2x=-0.71919, 1.2176
???