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已知cos2X=根号2/3,则sin^4X+cos^4的值为?求详细过程!

来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/05/13 06:34:42
已知cos2X=根号2/3,则sin^4X+cos^4的值为?求详细过程!
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
再问: sin^4x+2sin^2xcos^2x+cos^4x-2sin^2xcos^2x 怎么得到=(sin^2 2x+cos^2 2x)^2-(1/2)(2sinxcosx)^2 怎么X变成2X??
再答: sin^4x+2sin^2xcos^2x+cos^4x=[(sin^2(2x)+cos^2( 2x)]^2 (1/2)(2sinxcosx)^2=1/2*4*sin^2xcos^2x=2sin^2xcos^2x 明白了吗