已知cos2x=√ 2/3,则sin^4X+cos^4的值为?（我做的答案是-根号2/3,可没这选项）A13/18B11/18C7/9D-1sin^4X+cos^4x

已知cos2x=√ 2/3,则sin^4X+cos^4的值为?（我做的答案是-根号2/3,可没这选项）A13/18B11/18C7/9D-1sin^4X+cos^4x
已知cos2x=√ 2/3,则sin^4X+cos^4的值为?（我做的答案是-根号2/3,可没这选项）
A13/18
B11/18
C7/9
D-1
sin^4X+cos^4x

已知cos2x=√ 2/3,则sin^4X+cos^4的值为?（我做的答案是-根号2/3,可没这选项）A13/18B11/18C7/9D-1sin^4X+cos^4x
sin^4X+cos^4x
=(cos^2x+sin^2x)^2-1/2(2sinxcosx)^2
=1-1/2sin^2(2x)
=1-1/2[1-cos^2(2x)]
=1-1/2*[1-(√ 2/3)^2]
=1-1/2(1-2/9)
=1-1/2*7/9
=1-7/18
=11/18
选B

B
sin^4X+cos^4
=(cos^2x+sin^2x)^2-1/2(2sinxcosx)^2
=1-1/2sin^2(2x)
=1-1/2[1-cos^2(2x)]
=1/2+1/2*(√ 2/3)^2
=11/18

都是偶次方，怎么会是负数呢？再仔细算算吧