高1暑假作业数学题

高一数学暑假作业已知：sinx=

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...全部

  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 。
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