已知cos2X=根号2/3,则sin^4X+cos^4的值为?求详细过程!

网友回答

y=sin^4x+cos^4x
=sin^4x+2sin^2xcos^2x+cos^4x-2sin^2xcos^2x
=(sin^2 2x+cos^2 2x)^2-(1/2)(2sinxcosx)^2
=1-(1/2)(sin2x)^2
=1-(1/2)(1-cos^2 2x)
=1-1/2*(1-2/9)
=1-7/18
=11/18