sin^4x-sin^2xcos^2x+cos^4x =(sin^2x+cos^2x)^2-3sin^2xcos^2x

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/11/08 15:03:57

sin^4x-sin^2xcos^2x+cos^4x =(sin^2x+cos^2x)^2-3sin^2xcos^2x 那么这个依据呢?老师

针对三角函数的证明,一般都是采取化简的思路来解答.
对等式右边进行化简,
=(sin^2x+cos^2x)^2-3sin^2xcos^2x =（sin^4x+2sin^2xcos^2x+cos^4x）-3sin^2xcos^2x
=sin^4x-sin^2xcos^2x+cos^4x
=等式左边
所以sin^4x-sin^2xcos^2x+cos^4x =(sin^2x+cos^2x)^2-3sin^2xcos^2x 成立.

sin^2x+cos^2x)(sin^4x-sin^2xcos^2x+cos^4x) =sin^4x-sin^2xcos (1-(sin^4x-sin^2xcos^2x+cos^4x)/sin^2x +3sin^2x 化简cos^4x+sin^2xcos^2x+sin^2x 求函数f(x)=(sin^4x+cos^4x+sin^2xcos^2x)/2 求函数y=2sin xcos x+2sin x+2cos x+4的值域求sin^4x+cos^4x+4sin^2xcos^2x-1的最小正周期及值域. 求函数f（x）=（sin⁴x+cos⁴x+sin²xcos²x）/（2-si 证明sin4次方x+cos四次方x=1-2sin²xcos²x 已知函数f(x)=a(cos^2 x+sin xcos x)+b. 证明sin四次方x+cos四次方x=1-2sin平方xcos平方x f(x)=a(sin^6x+cos^6x)+b(sin^4x+cos^4x)+6sin^2xcos^2x的值与x无关且等求函数f(x)=sin^4x+cos^4x+sin^2xcos^2x/2-2sinxcosx-1/2sinxcosx+1