sin（x-y）

孙肥卓1274证明sin(x+y)sin(x - y)=(sinx)^2 - (siny)^2. -
籍逄类14777236452 ______[答案] sin(x+y)sin(x-y) =-1/2(cos(x+y+x-y)—cos(x+y-x+y)) =-1/2(cos2x—cos2y) =-1/2(1-2(sinx)^2-1+2(siny)^2) =(sinx)^2-(siny)^2

孙肥卓1274存在x,使得sin(x - y)=sinx - xiny,求证明 -
籍逄类14777236452 ______ 打错一个字母吧?存在x,使得sin(x-y)=sinx-siny 证:令x=2kπ,k∈Z,则sin2kπ=0,且sin(x-y)=sin(2kπ-y)=sin(-y)=-siny,即 存在x=2kπ,k∈Z,使 sin(x-y)=sinx-siny.

孙肥卓1274证明sin(x+y)sin(x - y)=sinx - siny -
籍逄类14777236452 ______ 解:sin(x+y)sin(x-y) =-1/2(cos(x+y+x-y)—cos(x+y-x+y)) =-1/2(cos2x—cos2y) =-1/2(1-2(sinx)^2-1+2(siny)^2) =(sinx)^2-(siny)^2

孙肥卓1274已知x,y为锐角,且cos(x+y)=sin(x - y)则tanx= -
籍逄类14777236452 ______ 解:∵cos(x+y)=sin(x-y) ==>cosxcosy-sinxsiny=sinxcosy-cosxsiny (应用和差角公式) ==>cosxcosy+cosxsiny=sinxcosy+sinxsiny ==>cosx(siny+cosy)=sinx(siny+cosy) ==>(sinx-cosx)(siny+cosy)=0 ∴sinx-cosx=0,或siny+cosy=0 ==>tanx=1,或tany=-1 ∵x,y为锐角,则00 ∴tany=-1不符合题意,应该舍去 故 必有tanx=1.

孙肥卓1274z=e^(2x)*sin(x - y),求dz -
籍逄类14777236452 ______[答案] ∂z/∂x=2e^(2x)*sin(x-y)+e^(2x)*cos(x-y) ∂z/∂y=-e^(2x)*cos(x-y) dz=[2e^(2x)*sin(x-y)+e^(2x)*cos(x-y)]dx-e^(2x)*cos(x-y)dy

孙肥卓1274sin(x - y)/sin(x+y)=2009/2010,求tanx/tany -
籍逄类14777236452 ______ sin(x-y)/sin(x+y)=(sinx*cosy-cosx*siny)/(sinx*cosy+cosx*siny) 1 tanx/tany=(sinx/cosx)*(siny/cosy)=(sinx*cosy)/(cosx*siny) 2 1式各项同除cosx*siny=[(sinx*cosy)/(cosx*siny)-1]/[(sinx*cosy)/(cosx*siny)+1] 3 假设z=tanx/tany=(sinx*cosy)/(cosx*siny) 则3式等于 (z-1)/(z+1)=2009/2010 4 求解4式得到 z=tanx/tany=4019

孙肥卓1274隐函数e^y=sin(x - y)的导数 -
籍逄类14777236452 ______ e^y=sin(x-y)e^y. y' =cos(x-y) .( 1-y')[e^y +cos(x-y)]y' = cos(x-y)y' =cos(x-y)/[e^y +cos(x-y)]

孙肥卓1274sin(x y)=2/3,sin(x - y)=1/5,则tanx/tany=?
籍逄类14777236452 ______ sin(x+y)=sinxcosy+cosxsiny=2/3 1式 sin(x-y)=sinxcosy-cosxsiny=1/5 2式 1式+2式 2sinxcosy=13/15 1式-2式 2cosxsiny=7/15 tanx/tany=(sinx/cosx)/(siny/cosy)=sinxcosy/cosxsiny=13/7

孙肥卓1274sin(x - y)=2sinxcosy 则x - y的最大值
籍逄类14777236452 ______ 2 sin x cos y = sin(x+y)+sin(x-y) 所以 sin(x-y)= sin(x+y)+sin(x-y), 0= sin(x+y), x+y=派的整数倍. 不能限制 x-y 的值

孙肥卓1274已知sinX=根号5/5,sin(X - Y)= - 根号10/10,X、Y均为锐角,则角Y等于 -
籍逄类14777236452 ______ ∵sinX=根号5/5,sin(X-Y)= - /10,X、Y均为锐角 ∴ cos x = 2根号5/5 , cos ( x - y ) = 3根号10/10 则 sin y = sin [ x - ( x - y ) ] = sin x cos ( x - y ) - cos x sin ( x - y ) = 根号2/2 ∴ y = π/4