(x^3 sin^2 x) (x^4 2x^2 1) dx

2sin^2[(π/4)+x]+根号3（sin^x-cos^x）-1=-(1-2sin^2[(π/4)+x)-√3cos2x=-cos(π/2+2x)-√3cos2x=sin2x-√3cos2x=2[

你好!题目可能有错,应该是x^4+2x^2+1才对吧!因为f(x)=x^3(sinx)^2/(x^4+2x^2+1)=x^3(sinx)^2/(x^2+1)^2那么f(-x)=-x^3(sinx)^2

那个前半括号里面相加等于一

2sin(x-π/4)sin(x+π/4)=cos(x-π/4-x-π/4)-cos(x-π/4+x+π/4)=-cos2xf(x)=cos(2x-π/3)-cos2x=cos(2x-π/6-π/6)

用公式a³+b³=(a+b)(a²-ab+b²)cos^6x+sin^6x=(cos²x)³+(sin²x)³=(cos

f(x)=cos(3x)*cos(2x)+sin(3x)*sin(2x)=cos(3x-2x)=cosxf'(x)=-sinx

由和差化积公式分子=2sin[(x^3+x^2)/2]cos[(x^3+x^2-2x)/2]x→0,则(x^3+x^2)/2→0,sin则(x^3+x^2)/2和(x^3+x^2)/2是等价无穷小而c

x=0:0.1:2*pi;s=2*sin(x)-sin(2*x)+2/3*sin(3*x)-1/2*sin(4*x)+2/5*sin(5*x);plot(x,s)

f(x)=sin(2x-π/6)=cos[π/2-(2x-π/6)]=cos(2π/3-2x)=cos(2x-2π/3),故f(x)为偶函数,且其关于x=π/3对称,周期为π,因此a的最小整数为π.

经济将积极

sinx+siny+sinz-sin(x+y+z)=4sin[(x+y)/2]sin[(x+z)/2]sin[(y+z)/2]sinx+siny+sinz-sin(x+y+z)=2sin[(x+y)/

hello!^-^令u=2x-π/6,则f（x）=sin(2x-π/6)=sinu=fu).因为-π/12≤x≤π/2,所以-π/3≤2x-π/6≤5π/6,即-π/3≤u≤5π/6.所以根据函数图像

f(x)=sin^2x+2√3sinxcosx+sin(x+π/4)sin(x-π/4)=(1-cos2x)/2+√3sin2x+(1/2)2sin(x-π/4)cos(x-π/4)=2-2cos2x

f（x）=cos（2x-π/3）+2sin（x-π)sin(x+π/4)=cos（2x-π/3)-√2sinx(sinx+cosx)=[(cos2x)/2]+[√3(sin2x)/2]-[√2(1-c

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

1、sinx=2分之根号2,或者cos(4x)=02、sinx=负二分之一,或者cosx=二分之一,或者cosx=0

已知函数f(x)=cos(2x-π/3)+2sin(x-π/4)sin(x+π/4)(1)求函数f(x)的最小正周期和图像的对称轴方程（2）求函数f(x)在区间[-π/12,π/2]上的值域⑴f(x)

sin^2(x)+cos^2(x+30)+sin(x)cos(x+30）=sin^2(x)+cos(x+30)[cos(x+30)+sinx]=sin^2(x)+cos(x+30)(cosxcos30

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