A^6 + B^6 = (A²+B²)(A^4-A²B²+B^4)
y=(sinx)^6 + (cosx)^6
=(sin²x+cos²x)(sin^4x-sin²xcos²x+cos^4x) (sin²x+cos²x)=1
= (sin^4x-sin²xcos²x+cos^4x) A^4-A²B²+B^4 = (A²+B²)²-3(AB)²
=(sin²x+cos²x)²-3(sinxcosx)² (sin²x+cos²x)=1
=1-3(sinxcosx)² sinxcosx = (sin2x)/2
=1-3(sin2x/2)²
=1-(3/4)(sin2x)^2 (sin2x)^2 = (1-cos4x)/2
=-(3/4)(1-cos4x)/2+1
=(3/8)cos4x+5/8 cosx周期是2π,cos4x周期是2π/4 = π/2
所以T=π/2
y最大則cos4x最大,當4x=2kπ時,cos4x最大是1
所以x=kπ/2,y= (3/8)+5/8 =1最大