我的世界各种工作台:数学高手帮帮忙

(tan10'-tan60')/(1/sin40')
= -(tan60'-tan10')/(1/cos50')
= -tan50'(1+tan10'tan60')cos50'
= -sin50'(1+tan10'tan60')
= -sin50'[1+sin10'sin60'/cos10'cos60']
= -sin50'[cos(60'-10')/cos10'cos60']
= -sin50'cos50'/cos10'cos60'
= -2sin50'cos50'/2cos10'cos60'
= -sin100'/cos10'
= -sin(90'+10')/cos10'
= -1

= -sin50'[1+sin10'sin60'/cos10'cos60']
= -sin50'[cos(60'-10')/cos10'cos60']
为什么这一步能得到下一步啊？

只知道是-1，计算器算的
三角函数忘得差不多了

tan10'-tan60')/(1/sin40')
= -(tan60'-tan10')/(1/cos50')
= -tan50'(1+tan10'tan60')cos50'
= -sin50'(1+tan10'tan60')
= -sin50'[1+sin10'sin60'/cos10'cos60']
= -sin50'[cos(60'-10')/cos10'cos60']
= -sin50'cos50'/cos10'cos60'
= -2sin50'cos50'/2cos10'cos60'
= -sin100'/cos10'
= -sin(90'+10')/cos10'
= -1
看步骤．方法，触类旁通．想直接答案电脑里的计算器直接能得到．

真是又勾起了那段伤心的回忆，又要重新去翻课本了，答案是：-1

通分啊....我的大哥大姐们!!!!!!!!
我就是 揉碎的岁月 啊...但是没有办法回答两次