已知sinx＋sinx2次方＝1,求cos2次方x＋cos6次方x的值

sinx＋sin^2x＝1,sinx=(-1+√5）/2
sinx=cos^2x
cos^2x＋cos^6x
=cos^2x(cos^4x+1)
=sinx(sin^2x+1)
=sinx(1-cos^2x+1)
=sinx(2-cos^2x)
=sinx(2-sinx)
=2sinx-sin^2x
=sinx+1
=1+(-1+√5）/2
=(1+√5）/2