高一数学三角函数化简：sin50du(1+genhao3tan10du)du是度数，genghao是根号，不好意思，弄错

sin50°*(1+根号3×tan10°)
=sin50°*(1+根号3*sin10°/cos10°)
=sin50°/cos10°*(cos10°+根号3*sin10°)
=2*sin50°/cos10°*(1/2*cos10°+根号 3/2*sin10°)
=2*sin50°/cos10°*(sin30°*cos10°
+cos30°*sin10°)
=(2*sin50°/cos10°)* sin40°
=(2*cos40°/cos10°)* sin40°
=(2* sin40°cos40°)/ cos10°
=sin80°/cos10°
=cos10°/cos10°
=1
=sin50[1+(sin60/cos60)*(sin10/cos10)]
=sin50[1+(sin60*sin10)/(cos60*cos10)]
=sin50[(sin10*sin60+cos10*cos60)/(cos10*cos60)]
=sin50[cos(60-10)/(cos10*cos60)]
=sin50[cos50/(cos10*cos60)]
=(sin50*cos50)/(cos10*cos60)
=sin100/(2*cos10*cos60)
=sin80/(2*cos10*cos60)
=cos10/(2*cos10*cos60)
=1/(2cos60)
=1