原式=[(tana+tanb)/(1-tanatanb)-(tana+tanb)]/[tana(tana+tanb)/(1-tanatanb)]
分子分母同除以tana+tanb
=[1/(1-tanatanb)-1]/[tana/(1-tanatanb)]
分子分母同乘以1-tanatanb
=[1-(1-tanatanb)]/tana
=tanatanb/tana
=tan
原式=[(tana+tanb)/(1-tanatanb)-(tana+tanb)]/[tana(tana+tanb)/(1-tanatanb)]
分子分母同除以tana+tanb
=[1/(1-tanatanb)-1]/[tana/(1-tanatanb)]
分子分母同乘以1-tanatanb
=[1-(1-tanatanb)]/tana
=tanatanb/tana
=tan