∫(-π 2~π 2)x^4sinx cosx

(1+cotx)sin^2x=sin^2x+sinxcosx2sin(x+π/4)sin(x-π/4)=根号2(sinx+cosx)*根号2/2(sinx-cosx)=sin^2x-cos^2xf(x

f(x)=cos^2x+sinxcosx=(1+cos2x)/2+1/2*sin2x=1/2+1/2(cos2x+sin2x)=√2/2*(√2/2*cos2x+√2/2sin2x)+1/2=√2/2

sin(PI/6+2x)=cos(PI/2-PI/6-2x)=cos(PI/3-2x)=cos(2*(PI/6-x))=1-2*sin(PI/6-x)^2=1-2*(1/4)^2=7/8tan70*c

积分值=（变量替换x＝pi/2-t)积分（0到pi/2）f(cosx)/(f(sinx)+f(cosx)),两者相加（就是两倍的积分值）,被积函数是1,故积分值是pi/2,因此原积分值是pi/4

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[

先用tanx=sinx/cosx、倍角公式、诱导公式化简原函数：f（x）=sin²x+sinxcosx-sin[2（x+π/4）]=（1-cos2x）/2+1/2sin2x-sin（2x+π

你得先把积分区域画出来,然后看图改变积分顺序.积分区域是y=x,y=√x,和y=2围成的区域.所以原式=∫（1,2）dy∫（y,y∧2）sin（πx/2y）dx=（4π8）/π∧3

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)

sin(π/4+x/2)sin(π/4-x/2)=sin(π/4+x/2)sin[π/2-(π/4+x/2)]∵π/4=π/2-π/4∴sin(π/4-x/2)=sin(π/2-π/4-x)=sin[

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

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

原式=[sinx*(-cosx)*sinx]/[(-cosx)*sinx*(-sinx)]=-1

f(x)=(1+1/tanx)*(sinx)^2-2sin(x+π/2)sin(x-π/4)=(1+cosx/sinx)*(sinx)^2+2sin(x+π/4)cos[(x-π/4)+π/2]=(s

【参考答案】D[sin(π/2-x)+sin(π-x)]/[cos(-x)+sin(2π-x)]=2009根据诱导公式,化简(cosx+sinx)/(cosx-sinx)=2009左边分子分母同时除以

ln(3+x)/(3-x)是奇函数,∫[-π/2,π/2]sin^2(x)*ln(3+x)/(3-x)dx=0∫[-π/2,π/2](sinx)^6dx=2∫[0,π/2](sinx)^6dx有公式=

证明：sin(π/4+x)/sin(π/4-x)+cos(π/4+x)/(π/4-x)?最后少了一个三角函数符号,请核对题目后追问.再问：sin(π/4+x)/sin(π/4-x)+cos(π/4+x