Question

高中数学三角函数第9题

Answer 1

|tanθ|=|-tan(180°-θ)|=|tan(180°-θ)|
lg|tan91°|+lg|tan92°|+...+lg|tan178°|+lg|tan179°|
=lg|tan89°|+lg|tan88°|+...+lg|tan2°|+lg|tan1°|
=lg|tan89°·tan88°·...·tan2°·tan1°|
=lg|(tan89°·tan1°)·(tan88°·tan2°)·...·(tan46°·tan44°)·tan45°|
=lg|(tan89°·cot89°)·(tan88°·cot88°)·...·(tan46°·cot46°)·tan45°|
=lg|1·1·...·1·1|
=lg1
=0

Answer 2

lgM+lgN=lg(MN)
原式=lg(|tan91°|*|tan92°|*...*|tan179°|） （括号里是1，理由看下面）
=lg1
=0

|tan91°|*|tan179|=1
|tan92°|*|tan178°|=1
....
|tan44°|*|tan46°|=1
|tan45°|=1