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°)
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/24 09:46:41
![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°)](/uploads/image/z/4028402-2-2.jpg?t=%E2%91%A0%E5%8C%96%E7%AE%801%2Bcos%28%CF%80%2F2+%2B%CE%B1%29%2Asin%28%CF%80%2F2+-%CE%B1%29%2Atan%28%CF%80%2B%CE%B1%29%E2%91%A1%E8%AE%A1%E7%AE%97%281%29tan%28%CF%80%2F5%29%2Btan%282%CF%80%2F5%29%2Btan%283%CF%80%2F5%29%2Btan%284%CF%80%2F5%29+%282%29sin%28-60%C2%B0%29%2Bcos%28225%C2%B0%29%2Btan135%C2%B0%283%29cos%28%CF%80%2F5%29%2Bcos%282%CF%80%2F5%29%2Bcos%283%CF%80%2F5%29%2Bcos%284%CF%80%2F5%29%EF%BC%884%EF%BC%89tan10%C2%B0%2Btan170%C2%B0%2Bsin1866%C2%B0-sin%28-606%C2%B0%29)
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°)
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°)
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°)
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
①由诱导公式得1-sina*cosa*tan*a=1-(sina)^2=(cosa)^2
②(1)由tana=-tan(π-a)得 原式=0
剩下都一样,自己想吧,要熟练掌握诱导公式