求函数f(x)=sin^6+cos^6的周期和最值

f(x)=(sin²x+cos²x)(sin⁴x-sin²xcos²x+cos⁴4)
=1*[(sin²x+cos²x)²-3sin²xcos²x]
=1²-3/4*(2sinxcosx)²
=1-3/4*sin²2x
=1-3/4*(1-cos4x)/2
=5/8+3/8*cos4x
所以T=2π/4=π/2
最大值=5/8+3/8=1
最小值5/8-3/8=1/4

f(x)=sin^6x+cos^6x
=(sin²x)³+(cos²x)³
=(sin²x+cos²x)(sin⁴x-sin²xcos²x+cos⁴x)
=1*(sin⁴x+2sin²xcos²x+cos⁴x-3sin²...

f(x)=sin^6x+cos^6x=(sin^2x+cos^x)(sin^4x-sin^2x*cos^2x+cos^4x)
=sin^4x-sin^2x*cos^2x+cos^4x=sin^4x+2sin^x*cos^2x+cos^4x-3sin^2x*cos^2x
=(sin^2x+cos^2x)^2-3/4sin^2(2x)
=1-3/8(1-cos4x)
=3/8*cos4x+5/8
周期T=2π/w=2π/4=π/2
最大值 1 当cos4x=1时
最小值 1/4当cos4x=-1时

你好，很高兴回答你的问题
①周期
sin^6(x)+cos^6(x)=[sin^2(x)]^3+[cos^2(x)}^3
=[sin^2(x)+cos^2(x)}*[sin^4(x)]+[cos^4(x)-sin^2(x)cos^2}
=1*[sin^4(x)]^3+[cos^4(x)-sin^2(x)cos^2}
=[sin^2(x)]^+cos^^2(x...