易知0＜x＜30°
sin(50°-x)sin²x
=sinxsin(100°-x)sin(30°-x)
∵sinx＞0
∴sin(x-50°)sinx=sin(x+80°)sin(x-30°)
cos(2x-50°)-cos50°
=cos(2x+50°)-cos110°
cos(2x-50°)-cos(2x+50°)
=cos50°-cos110°
→sin2x*sin50°=sin80°sin30°
→sin2xcos40°=2sin40°cos40°*1/2
→sin2x=sin40°
又0＜x＜30° ∴2x=40°
→x=20°