tan10°+tan50°=sin(10+50)/(cos10*cos50)=sin60/(cos10cos50)=根号3/(2cos10cos50)
tan60°-tan60°tan10°tan50°
=tan60(1-tan10tan50)
=tan60(1-sin10sin50/cos10cos50)
=tan60(cos10cos50-sin10sin50)/cos10cos50
=tan60*cos(10+50)/cos10cos50
=(sin60/cos60)*cos60/cos10cos50
=sin60/cos10cos50
=根号3/(2cos10cos50)
所以：tan10°+tan50°=tan60°-tan60°tan10°tan50°