化简sin(2π-α)/cos(3π/2-α)化简

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/20 13:28:19
化简sin(2π-α)/cos(3π/2-α)化简

化简sin(2π-α)/cos(3π/2-α)化简
化简sin(2π-α)/cos(3π/2-α)
化简

化简sin(2π-α)/cos(3π/2-α)化简
原式=-sina/-sina=1

很好办,你令θ=0,或令θ=2π算出的结果即所求,这叫特殊值法,你可 以多取几个特殊值,以防万一

=sin(2π + (-θ)]/cos[2π - (θ + π/2)]

=sin(-θ) /cos[π/2 + θ]

=sin(-θ) /cos[π/2 - (-θ)]

=sin(-θ) /sin(-θ)

=1

注,这里用到了几个公式:

  1. sin(α + 2kπ) = sinα

  2. cos(α + 2kπ) = cosα

  3. cos(π/2 - α) = sinα

     

化简:sin(2π-α)cos(π+α)cos(11π/2-α)/cos(π-α)sin(3π-α)sin(-π-α)sin(9π/2+α) 化简sin(-π/2-α)sin(πα)cos(-α-π)/cos(π-α)sin(3π α) (1+sinα+cosα)*[sin(α/2)-cos(α/2)]/√(2+2cosα)化简 (3/2*π 求值:(tan10°-√3)×cos10°/sin50° 求证:[sin(2α+β)]/sinα- 2cos(α+β)=sinβ/cosα 化简cosθ+cos(θ+2π/3)+cos(θ+4π/3) 证明:sin(α+β)sin(α-β)=sin^2α-sin^2β 设角a=-35π/6,则2sin(π+α)cos(π-α)-cos(π+α)/ 1+sin^2α+sin(π-α)-cos^2(π+α)sina=sin(-35π/6)=sin(-6π+π/6)=1/2 cosα=根号3/22sin(π+α)cos(π-α)-cos(π+α)/ [1+sin^2α+sin(π-α)-cos^2(π+α)]=2(-sinα)(-cosα)+cosα/[1+sin² 化简:2sinα^2cosα-sin(3/2π-α)cos2α= 化简[sin(π/2-α)cos(π/2-α)]/cos(π+α)-[sin(π-α)cos(π/2-α)]/sin(π+α) 已知6sin²α+sinαcosα-2cos²α=0,α∈(π/2,π),求值1).(sinα-3cosα)/(sinα-cosα);2).sinαcosα-sin²α;3).sin²α-3cosαsinα-2 化简sin(α-5π)/cos(3π-α)×cos(π/2-α)/sin(α-3π)×cos(8π-α)/sin(-α-4π) 【三角函数】已知sin(α-π)=2cos(2π-α),求[sin(π-α)+5cos(2π-α)]/[3cos(π-α)-sin(-α)] 若sin(α-π)=2cos(2π-α),求(sinα+5cosα)/(sinα-3cosα)的值, 化简sin(α-2π)+sin(-a-3π)cos(α-3π)/cos(π-α)-cos(-π-α)cos(α-4π) 已知tan(3π+α)=2,求:1、(sinα+cosα)²;2、sinα-cosα/2sinα+cosα 已知tan(π-α)=2,求sin²α-2sinαcosα-cos²α/4cos²α-3sin²α+1 已知tan(π-α)=2,求sinα-2sinαcosα-cosα/4cosα-3sinα的值 若(sinα+cosα)/(sinα-cosα)=2 则sin(α-5π)·sin(3π/2-α)=? 若sinα+cosα/sinα-cosα=2,则sin(α-5π)*sin(3π/2-α)等于? 化简cos(3/2π+π)sin(-π+α)