难度很高很高很高*N的数学题目```

来源：百度知道 编辑：UC知道 时间：2024/05/25 19:28:30
cos^6 x+sin^6 x的最小周期是？
要过程``
谢谢``

∏／2
原式＝(cos^2x+sin^2x)(cos^4x+sin^4x-cos^2xsin^2x)
=cos^4x+sin^4x-cos^2xsin^2x
=(cos^2x+sin^2x)^2-3cos^2xsin^2x
=-3cos^2xsin^2x
=(-3/4)(sin2x)^2
剩你的会算了吧

4(cos^6 x +sin^6 x)
=4(cos^2x+sin^2x)(cos^4x-cos^2xsin^2x+sin^4x)
=4[(cos^2x+sin^2x)^2-3cos^2xsin^2x]
=4[1-3cos^2xsin^2x]
=4[1-3/2*sin^2(2x)]
=4{1-3/2*[1-cos(4x)]/2}
由此可知，最小正周期为2pi/4=1/2*pi