f(x)=a(sin^6x+cos^6x)+b(sin^4x+cos^4x)+6sin^2xcos^2x的值与x无关且等
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f(x)=a(sin^6x+cos^6x)+b(sin^4x+cos^4x)+6sin^2xcos^2x的值与x无关且等于1
f(x)=a(sin²x+cos²x)(sin^4x-sin²xcos²x+cos^4x)+b(sin^4x+cos^4x)+6sin^2xcos^2x
=a(sin^4x-sin²xcos²x+cos^4x)+b(sin^4x+cos^4x)+6sin^2xcos^2x
=(a+b)(sin^4x+cos^4x)+(6-a)sin^2xcos^2x
=(a+b)[(sin²x+cos²x)²-2sin^2xcos^2x]+(6-a)sin^2xcos^2x
=(a+b)(1-2sin^2xcos^2x)+(6-a)sin^2xcos^2x
=(a+b)+(6-a-2a-2b)sin^2xcos^2x
和x无关且等于1
所以a+b=1
6-a-2a-2b=0
a=4,b=-3
=a(sin^4x-sin²xcos²x+cos^4x)+b(sin^4x+cos^4x)+6sin^2xcos^2x
=(a+b)(sin^4x+cos^4x)+(6-a)sin^2xcos^2x
=(a+b)[(sin²x+cos²x)²-2sin^2xcos^2x]+(6-a)sin^2xcos^2x
=(a+b)(1-2sin^2xcos^2x)+(6-a)sin^2xcos^2x
=(a+b)+(6-a-2a-2b)sin^2xcos^2x
和x无关且等于1
所以a+b=1
6-a-2a-2b=0
a=4,b=-3
f(x)=a(sin^6x+cos^6x)+b(sin^4x+cos^4x)+6sin^2xcos^2x的值与x无关且等
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