①化简1+cos(π/2 +α)*sin(π/2 -α)*tan(π+α)

题目

①化简1+cos(π/2 +α)*sin(π/2 -α)*tan(π+α)
②计算(1)tan(π/5)+tan(2π/5)+tan(3π/5)+tan(4π/5)
(2)sin(-60°)+cos(225°)+tan135°
(3)cos(π/5)+cos(2π/5)+cos(3π/5)+cos(4π/5)
（4）tan10°+tan170°+sin1866°-sin(-606°)

答案

第一问：根据诱导公式：
1+cos(π/2 +α)*sin(π/2 -α)*tan(π+α)
=1+sinαcosα×（-sinα/cosα）
=1-sin^2α
第二问：
使用和差化积公式
tan(π/5)+tan(2π/5)+tan(3π/5)+tan(4π/5)
=sin(π)/cos(π/5)×cos(4π/5)+sin(π)/cos(2π/5)×cos(3π/5）
=0
2.使用诱导公式
sin(-60°)+cos(225°)+tan135°
=-√3/2-√2/2-1
3.使用和差化积公式
cos(π/5)+cos(2π/5)+cos(3π/5)+cos(4π/5)
=2cos(π/2)cos(3π/10)+2cos(π/2)cos(π/10)
=0
4.使用和差化积公式
tan10°+tan170°+sin1866°-sin(-606°)
=sin(π)/cos10°cos170°+0
=0
祝：楼主学业进步