The expression (cos20° − cos40°)/(sin20° + sin40°) equals:

cosC − cosD = 2·sin((C + D)/2)·sin((D − C)/2) gives 2·sin30°·sin10°, and sinC + sinD = 2·sin((C + D)/2)·cos((D − C)/2) gives 2·sin30°·cos10°. The common factor cancels, leaving tan10° ≈ 0.176. Check: 0.1736/0.9848 = 0.176.