已知：sinx=4sin(x+y).求证：tan(x+y)=siny/(cosy-4)
热心网友
sinx=4sinx+y)---sin[(x+y)-y]=4sin(x+y)---sin(x+y)cosy-cos(x+y)siny=4sin(x+y)---sin(x+y)(cosy-4)=cos(x+y)siny---sin(x+y)/cos(x+y)=siny/(cosy-4)---tan(x+y)=siny/(cosy-4)
热心网友
sinx=4sinx+y)---sin[(x+y)-y]=4sin(x+y)---sin(x+y)cosy-cos(x+y)siny=4sin(x+y)---sin(x+y)(cosy-4)=cos(x+y)siny---sin(x+y)/cos(x+y)=siny/(cosy-4)---tan(x+y)=siny/(cosy-4)
热心网友
tan(x+y)*(cosy-4)=sin(x+y)*(cosy-4)/cos(x+y)=[cosy*sin(x+y)-4sin(x+y)]/cos(x+y)=[cosy*sin(x+y)-sinx]/cos(x+y) 已知:sinx=4sin(x+y)=[sin(90-y)*sin(x+y)-sinx]/cos(x+y)={(-1/2)*[cos(90-y+x+y)-cos(90-y-x-y)]-sinx}/cos(x+y)={(-1/2)*[cos(90+x)-cos(90-y-x-y)]-sinx}/cos(x+y)={(-1/2)*[-sinx-sin(x+2y)]-sinx}/cos(x+y)={(1/2)*[sinx+sin(x+2y)]-sinx}/cos(x+y)=(1/2)*[sin(x+2y)-sinx]/cos(x+y)=(1/2)*{2[cos(x+2y+x)/2]*[sin(x+2y-x)/2]}/cos(x+y)=(1/2)*[2cos(x+y)*siny]/cos(x+y)=cos(x+y)*siny/cos(x+y)=siny∵tan(x+y)*(cosy-4)=siny∴tan(x+y)=siny/(cosy-4)得证。