cos(x+y)

汲冒郑5189y=cos(x+y)求导 -
辕详狮18353027487 ______ 解:y=cos(x+y)dy/dx=-sin(x+y)(1+dy/dx)

汲冒郑5189【高中数学】已知cos(x+y)=1/3,cos(x - y)=2/3,且0 -
辕详狮18353027487 ______[答案] 0π/3-π/3所以sin(x+y)=2根号2/3,sin(x-y)=-根号5/3 所以 cos2x =cos(x+x+y-y) =cos(x+y+x-y) =cos(x+y)cos(x-y)-sin(x+y)sin(x-y) =2/9+2根号10/9 =2/9(1-根号10)

汲冒郑5189y=sin(x+y)求导中的1 - cos(x+y)是怎么来的 -
辕详狮18353027487 ______[答案] 对x求导 则y'=cos(x+y)*(x+y)' y'=cos(x+y)*(1+y') 所以y'=cos(x+y)+y'cos(x+y) 移项就有了y'[1-cos(x+y)]=cos(x+y) y'=cos(x+y)/[1-cos(x+y)]

汲冒郑5189求由e^y=cos(x+y)所确定的隐函数y=y(x)的导数 -
辕详狮18353027487 ______[答案] e^y=cos(x+y) (e^y).y' = -sin(x+y) .( 1+ y') (e^y + sin(x+y) ) y' = -sin(x+y) y' =-sin(x+y)/(e^y + sin(x+y) )

汲冒郑5189证明COS(X+Y)COS(X - Y)=COS^2X - SIN^2Y -
辕详狮18353027487 ______ COS(X+Y)COS(X-Y)=(COSX*COSY-SINX*SINY)(COSX*COSY+SINX*SINY)=(COSX*COSY)^2-(SINX*SINY)^2=COS^2 X(1-SIN^2 Y)-(1-COS^2 X)SIN^2 Y=COS^2 X -COS^2 X*SIN^2 Y-SIN^2 Y +COS^2 X SIN^2 Y=COS^2X-SIN^2Y

汲冒郑5189cos(x +y) - cos(x)= -
辕详狮18353027487 ______[答案] 和差化积公式 cos(x +y)-cos(x)=-2sin(y/2)sin[x+(y/2)]

汲冒郑5189若cos(x+y)cos(x - y)=⅓,则(cos^2)x - (sin^2)y= -
辕详狮18353027487 ______[答案] 分析, cos(x+y)=cosx*cosy-sinx*siny cos(x-y)=cosx*cosy+sinx*siny ∴cos(x+y)*cos(x-y)=1/3 cos²x*cos²y-sin²x*sin²y=1/3 cos²x*(1-sin²y)-(1-cos²x)*sin²y=1/3 -cos²x*sin²y+cos²x-sin²y+cos²x*sin²y=1/3 cos²x-sin²y=1/3.

汲冒郑5189求证COS(x+y)COS(x - y)=COS2x - SIN2y
辕详狮18353027487 ______ zhengming: cos(x+y)=cosxcosy-sinxsiny cos(x-y)=cosxcosy+sinxsiny所以,二者相乘以后=cosxcoxcosycosy-sinxinxsinysiny=(1-sinxsinx)cosycosy-sinxsinxsinysiny=cos2x-sin2y

汲冒郑5189y=cos(x+y) y对x的导数y=cos(x+y) y对x的导数 -
辕详狮18353027487 ______[答案] y'=-sin(x+y)*(x+y)' y'=-sin(x+y)*(1+y') y'/(1+y')=-sin(x+y) y'=-sin(x+y)/(1+sin(x+y))

汲冒郑5189cosx=1/3,cos(x+y)= - 3/5,且x,y都是锐角,则cosy=, -
辕详狮18353027487 ______[答案] x是锐角 sinx>0 sin²x+cos²x=1 sinx=2√2/3 0cos(x+y)=-3/5 所以sin(x+y)=4/5 cosy=cos[(x+y)-x] =cos(x+y)cosy+sin(x+y)siny =(8√2-3)/15