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Cos(x+x)=CosxCosx%sinxsinx的推导过程

1、根据公式:cos(A+B)=cosA*cosB-sinA*sinB, 令A=B=X,可得公式。 2、从原始知识开始推导: 先建立直角坐标系,在直角坐标系xOy中作单位圆O,并作出角a,b,与-b,使角a的开边为Ox,交圆O于点P1,终边交圆O于点P2,角b的始边为OP2,终边交圆O于...

有个公式cos(a+b)=cosacosb-sinasinb 则 cos2x=cos(x+x)=cosxcosx-sinxsinx

∵0

解:sinxsinx+sinxcosx =根号2sinx(sinxcosπ/4+sinπ/4cosx)=根号2sinxcos(x+π/4)

这类题,一般都是换元法,设cosx=t,-1

原式=√2(sinxcos45+sin45cosx)=√2sin(x+45)

解答: 化成y=Asin(wx+∅)的形式 f(x)=cosx(cosx+sinx) =cos²x+sinxcosx =(cos2x+1)/2+(sin2x)/2 =(√2/2)*[sin2x*(√2/2)+cos2x*(√2/2)]+1/2 =(√2/2)*[sin2x*cos(π/4)+cos2x*sin(π/4)]+1/2 =(√2/2)sin(2x+π/4)+1/2 ∴ 最大值是√2/2+1/2

①cos(-60°)=cos60°=12,命题错误;②sin75°=sin(30°+45°)=sin30°?cos45°+cos30°?sin45°=12×22+32×22=24+64=6+24,命题正确;③sin2x=sinx?cosx+cosx?sinx=2sinx?c

sin(x-y)^2 = 1 - cos(x-y)^2 = 1 - cosxcosy^2 - sinxsiny^2 -2sinxsinycosxcosy 1=sinx^2 + cosx^2 即sin(x-y)^2=sinx^2(1-siny^2)+cosx^2(1-cosy^2) -2sinxsinycosxcosy =sinxcosy^2 + cosxsiny^2 - 2sinxsinycosxcosy =(sinxcosy-cosxsiny)...

三角函数诱导公式:cos(π/2-α)=sinα sin(π/2-α)=cosα cos(π/2+α)=-sinα sin(π/2+α)=cosα

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