y=cos²x 4sinx的最值及取到最值时x的集合

y=cosX+cos(X-π/3)=cosX+cosX*1/2+sinX*(√3)/2=cosX*3/2+sinX*(√3)/2=3sin(X+β)∴最小值：-3最大值：3

把平方打开,y=根号下（sina)^2+(cosa)^2+2(sina-cosa)+2=根号下2（sina-cosa)+3=根号下（2根号2×sin(a-π／4）+3）所以,最小值为：根号下3-2根号

可以根据：asinα+bcosα=√(a^2+b^2)*sin(α+θ),其中θ由a,b的符号和tanθ=b/a确定具体到这题,就是：y=√[(√3+2)/2]^2+(1/2)^2*sin(2x+θ)

sinx+siny=1/3sinx=1/3-siny(siny)^2+(cosy)^2=1(cosy)^2=1-(siny)^2u=sinx-cos^2yu=(1/3-siny)-[1-(siny)^

sinx的取值范围是【-1,1】又siny=1/3-sinx所以可以得到siny的取值范围是【-2/3,4/3】又siny本身的取值范围是【-1,1】故可以得到siny的取值范围是【-2/3,1】u=

y=sin²x+cos²x+2sinxcosx+2cos²x-1+1=1+sin2x+cos2x+1=√2sin(2x+π/4)+2-1

y=[(sinx)^2+(cosx)^2]^2-2(sinx)^2(cosx)^2=1-2(sinx*cosx)^2=1-2*(sin2x/2)^2=1-(sin2x)^2/2=1-(1-cos4x)

sin^2x+cos^2y=1/2∴sin^2x=1/2-cos^2y3sin^2x+sin^2y=3（1/2-cos^2y）+sin^2y=1.5-3cos^2y）+sin^2y又有sin^2y+c

y=sin^2x+2sinxcosx+3cos^2x=sin^2x+2sinxcosx+cos^2x+2cos^2x=1+sin2x+2cos^2x-1+1=sin2x+cos2x+2=√2(√2/2

y=cos^2x-sin^2-√3cos(3π/2+2x)+1=cos2x-√3sin2x+1=2cos(2x+π/3)+1当2kπ+π/2≤2x+π/3≤2kπ+3π/2时,函数单调递减2kπ+π/

=cos²x+sinx=1-sin²x+sinx=-sin²x+sinx-1/4+1/4+1=-(sinx-(1/2))²+(5/4)当|x|≤π/4,-√2/

最小正周期π最大值2最小值0

y=2cos^2[(x+1)/2]=1+cos(x+1)T=2π最大值2最小值0

y=sin^2(x)+2sin(x)cos(x)+3cos^2(x)=1+2cos^2(x)+sin2x=2+sin2x+cos2x构造向量a=（sin2x,cos2x）,b=（1,1）a+b=（si

和差化积得y=2cos(x-π/6)cosπ/6=√3cos(x-π/6).故ymin=-√3,ymax=√3.

y=(sinχ+cosχ）²+2cos²χ求导得：y‘=2(sinx+cosx)(cosx-sinx)-4cosxsinx=2(cos²x-sin²x)-2si

y=cos²x－sinxcosx=1/2(1+cos2x)-1/2sin2x=1/2cos2x-1/2sin2x+1/2=√2/2(√2/2*cos2x-√2/2*sin2x)+1/2=√2

y=cosx*(-2)sin[(x+x+2/3)/2]sin[(-2/3)/2]=2cosxsin(x+1/3)sin(1/3)=2sin(1/3)cosxsin(x+1/3)=2sin(1/3)(1

y=(sinx)^2+3(cosx)^2+2sinxcosx=2+2(cosx)^2+2sinxcosx=2+cos2x+1+sin2x=3+sin2x+cos2x=√2sin(2x+π/4)+3最大

y=2asinx-cos²x+a²+2=2asinx+sin²x+a²+1=(sinx+a)²+1当a>=0时最小值为f(x)=(a-1)²