cos50°（√3-tan10°）
=[cos(90°-40°)]{√3 -[(1-cos20°)/sin20°]}
=sin40°{√3 -[(1-cos20°)/sin20°]}
=(√3sin40°) - [(2sin20°cos20°)(1-cos20°)/sin20°]
=(√3sin40°) - [2cos20°- 2(cos20°)^2]
=(√3sin40°) - 2cos20°+ (cos40°+1)
=2[(1/2)cos40°+ (√3/2)sin40°] - 2cos20°+ 1
=2[cos60°cos40°+ sin60°sin40°] - 2cos20°+ 1
=2cos(60°-40°) - 2cos20°+ 1
=2cos20°- 2cos20°+ 1
=1