2(sin^6x+cos^6)-3(sin^4x+cos^4x)

来源：学生作业帮编辑：大师作文网作业帮分类：数学作业时间：2024/11/12 09:50:51

sin^6x+cos^6x=(sin^2x+cos^2x)(sin^4x-sin^2xcos^2x+cos^4x)
=sin^4x-sin^2xcos^2x+cos^4x
=(sin^2x+cos^2x)^2-3sin^2xcos^2x
=1-3sin^2xcos^2x
sin^4x+cos^4x=(sin^2x+cos^2x)^2-2sin^2xcos^2x
=1--2sin^2xcos^2x
2(sin^6x+cos^6)-3(sin^4x+cos^4x)=2(1-3sin^2xcos^2x)-3(1--2sin^2xcos^2x)
=-1

三角等式求证：cos^6x+sin^6x=1-3sin^2x+3sin^4x 化简[1-(sin^4x-sin^2cos^2x+cos^4x)/(sin^2)]+3sin^2x 证明sin^2(x)+cos^2(x+30)+sin(x)cos(x+30)=3/4 三角函数证明及化简题1.证明sin^6x＋cos^6x＝（sin^2x＋cos^2x)（cos^4x－cos^2xsin (1-(sin^4x-sin^2xcos^2x+cos^4x)/sin^2x +3sin^2x 化简（1)√3sin x+cos x (2）√2(sin x-cos x) （3）√2cos x-√6sin x 用cos x表示sin^4 x -sin^2 x +cos^2 x 已知函数f(x)=cos(2x-π/3）+2sin(x-π/4）sin(x+π/4)=sin(2x-π/6) , 求证（cos^2 x-sin^2 x)(cos^4 x+sin^4 x)+1/4 sin 2x sin 4x=cos 2 sin^2x+cos^2x)(sin^4x-sin^2xcos^2x+cos^4x) =sin^4x-sin^2xcos 已知cos 2x=3/5,求sin^4 x+cos^4 x的值化简sin(3π-x)cos(x-3/2)cos(4π-x)/tan(x-5π)cos(π/2+x)sin(x-5/2π