若sin^2α+sinα=1 则cos^4α+cos^2α=
问题描述:
若sin^2α+sinα=1 则cos^4α+cos^2α=
答
由sin^2α+sinα=1及sin^2a+cos^2a=1知cos^2a=sina
cos^4α+cos^2α= cos^2a(cos^2a+1)=sina(sina+1)=sin^2a+sina=1
答
(sina)^2+sina=1
(sina)^2=1-sina
(cosa)^2=1-(sina)^2=1-1+sina=sina
(cosa)^4=(sina)^2
(cosa)^4+(cosa)^2=(sina)^2+sina=1