诱导公式计算问题,急,计算tan（-36π/6）×sin(-46π/3)-cos37π/6×tan55π/6怎么分解里面的?化简后符号到底怎么判断?tan(6π-35π/6)×-sin（16π-46π/3）-cos（6π-37π/6）×tan（9π-55π/6）过程是这样对吗?那

Question

诱导公式计算问题,急,
计算tan（-36π/6）×sin(-46π/3)-cos37π/6×tan55π/6
怎么分解里面的?化简后符号到底怎么判断?
tan(6π- 35π/6)×-sin（16π -46π/3）-cos（6π -37π/6）×tan（9π-55π/6）过程是这样对吗?那么怎么判断符号?2π倍的不看,那么后面的弧度怎么判断符号?如果化成角度太大了也不好看?麻烦解释下符号的问题,就这道题而言,

Answer 1

原式=tan(π/6-6π)·sin(2π/3-16π)-cos(π/6+6π)·tan(π/6+6π)
=tan(π/6)·sin(2π/3)-cos(π/6)·tan(π/6)
=tan(π/6)·sin(π/3)-cos(π/6)·tan(π/6)
=tan(π/6)·cos(π/6)-cos(π/6)·tan(π/6)
=0