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
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![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](/uploads/image/z/7172691-51-1.jpg?t=%E5%B7%B2%E7%9F%A5cos2x%3D%E2%88%9A+2%2F3%2C%E5%88%99sin%5E4X%2Bcos%5E4%E7%9A%84%E5%80%BC%E4%B8%BA%3F%EF%BC%88%E6%88%91%E5%81%9A%E7%9A%84%E7%AD%94%E6%A1%88%E6%98%AF-%E6%A0%B9%E5%8F%B72%2F3%2C%E5%8F%AF%E6%B2%A1%E8%BF%99%E9%80%89%E9%A1%B9%EF%BC%89A13%2F18B11%2F18C7%2F9D-1sin%5E4X%2Bcos%5E4x)
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