已知(sinα+cosα)/(sinα-cosα)=3求2sin^2α+((sinα-cosα)^2的值

显示全部楼层 · 2011-8-25 18:11:27

(sinα+cosα)/(sinα-cosα)=3(tanx+1)/(tanx-1)=3tanx=22sin2α+(sinα-cosα)2=[2sin2α+(sinα-cosα)2]/(sin2α+cos2α)=[2tan2α+(tanα-1)2]/(tan2α+1)=[8+1]/(4+1)=9/5...

千问 · 2011-8-25 18:11:27

[(sinα+cosα)/(sinα-cosα)]^2=3^2化简整理得：sin2a=4/5所以：cos2a=3/5 或cos2a=-3/52sin^2α+((sinα-cosα)^2=2sin^2α+sin^2α-2sinaicosa+cos^2α=2sin^2α+1-sin2a=-cos2a+2-sin2a当cos2a=3/5...

千问 · 2011-8-25 18:11:27

(sina+cosa)/(sina-cosa)=3(tana+1)/(tana-1)=3tana+1=3tana-32tana=4tana=2cos2a=(1-tan2a)/(1+tan2a)=(1-4)/(1+4)=-3/5sin2a=2tana/(1+tan2a)=4/52sin2a+(sina-co...

千问 · 2011-8-25 18:11:27

(sinα+cosα)/(sinα-cosα)=3容易得到sina=2cosa ，tana=2，sina=2/根号5，cosa=1/根号5或者sina=-2/根号5，cosa=-1/根号5所以2sin^2α+((sinα-cosα)^2=8/5+1/5=9/5...