对k∈Z,设sin(2kπ+α)与cos(2kπ+α)是方程2x²+(根号2+1)x+5m=0的两根求m与sin/(1-/tanα)+cosα/(1-tanα)的值

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/16 07:54:24
对k∈Z,设sin(2kπ+α)与cos(2kπ+α)是方程2x²+(根号2+1)x+5m=0的两根求m与sin/(1-/tanα)+cosα/(1-tanα)的值

对k∈Z,设sin(2kπ+α)与cos(2kπ+α)是方程2x²+(根号2+1)x+5m=0的两根求m与sin/(1-/tanα)+cosα/(1-tanα)的值
对k∈Z,设sin(2kπ+α)与cos(2kπ+α)是方程2x²+(根号2+1)x+5m=0的两根
求m与sin/(1-/tanα)+cosα/(1-tanα)的值

对k∈Z,设sin(2kπ+α)与cos(2kπ+α)是方程2x²+(根号2+1)x+5m=0的两根求m与sin/(1-/tanα)+cosα/(1-tanα)的值
sin(2kπ+α)=sinα cos(2kπ+α)=cosα
由韦达定理得
sinα+cosα=-(√2+1)/2
sinαcosα=5m/2
(sinα+cosα)²=[-(√2+1)/2]²
sin²α+cos²α+2sinαcosα=(3+2√2)/4
5m+1=(3+2√2)/4
m=(2√2-1)/20
sinα/(1- 1/tanα) +cosα/(1-tanα)
=sinα/(1- cosα/sinα) +cosα/(1- sinα/cosα)
=sin²α/(sinα-cosα)+cos²α/(cosα-sinα)
=sin²α/(sinα-cosα)-cos²α/(sinα-cosα)
=(sin²α-cos²α)/(sinα-cosα)
=(sinα+cosα)(sinα-cosα)/(sinα-cosα)
=sinα+cosα
=-(1+√2)/2

sin(2kπ+α)与cos(2kπ+α)是方程2x²+(根号2+1)x+5m=0的两根
sin(2kπ+α)+cos(2kπ+α)=-√2-1,
sin(2kπ+α)cos(2kπ+α)=5m
sinα+cosα=-√2-1……(1)
sinαcosα=5m……(2)
(1)平方得:1+2sinαcosα=3+2√2
10m=2+2√2<...

全部展开

sin(2kπ+α)与cos(2kπ+α)是方程2x²+(根号2+1)x+5m=0的两根
sin(2kπ+α)+cos(2kπ+α)=-√2-1,
sin(2kπ+α)cos(2kπ+α)=5m
sinα+cosα=-√2-1……(1)
sinαcosα=5m……(2)
(1)平方得:1+2sinαcosα=3+2√2
10m=2+2√2
m=0.2+0.2√2
sinα/(1-1/tanα)+cosα/(1-tanα)
=sinαsinα/(sinα-cosα)+cosαcosα/(cosα-sinα)
=(sinα+cosα)(sinα-cosα)/(sinα-cosα)
=sinα+cosα
=-√2-1

收起

对k∈Z,设sin(2kπ+α)与cos(2kπ+α)是方程2x²+(根号2+1)x+5m=0的两根求m与sin/(1-/tanα)+cosα/(1-tanα)的值 已知sin^4α+cos^4α=1,求:sin^kα+cos^kα(k∈Z). 弧度制下的角的表示sin(2kπ+α)=sinα (k∈Z)  cos(2kπ+α)=cosα (k∈Z)  tan(2kπ+α)=tanα (k∈Z)  cot(2kπ+α)=cotα (k∈Z)  sec(2kπ+α)=secα (k∈Z)  csc(2kπ+α)=cscα 求证(1-cosα)/sinα=sinα/(1+cosα)=tan(α/2)(α≠kπ,k∈z) 快回答! 求证:(sin(kπ-α)cos(kπ+α))/(sin((k+1)π+α)cos((k+1)π+α))=-1,k∈Z sin(kπ-α)*cos〔(k-1)π-α〕/sin〔(k+1)π+α〕*cos(kπ+α) ,k属于Z 化简:sin[(k+1)π+θ]×cos[(k+1)π-θ] / sin(kπ-θ)×cos(kπ+θ) (k∈Z) 化简 sin[(k+1)π+θ]*cos[(k+1)π-θ]/sin(kπ-θ)*cos(kπ+θ) k∈z 化简 {sin[α+(k+1)π]+sin[α-(k+1)π]}/[sin(α+kπ)*cos(α-kπ)],k∈Z 已知tanα=2 若α是第三象限角,求sin(kπ-α)+cos(kπ+α)(k∈z)的值 设P={cos nπ/3,n∈Z},Q={sin(2k-3)π/6,k∈Z}.则集合P与Q的关系是:烦请分析一下! 设α角的终边上一点P的坐标是(cosπ/5,sinπ/5),则α等于多少?答案为2kπ-9π/5(k∈z) 已知θ≠kπ(k∈Z)求证:tan(θ/2)=(1-cosθ)/sinθ 当2kπ-π/4≤α≤2kπ+π/4(k∈Z),化简√(1-2sinα×cosα)+√(1+2sinα×cosα) 若α∈(-π/2+2kπ,2kπ)(k∈Z),则sinα,cosα,tanα的大小关系是A.tanα>sinα>cosαB.tanα>cosα>sinαC.tanα<sinα<cosαD.tanα<cosα<sinα 设α角的终边上一点P的坐标(sinπ/3,cosπ/3),则α等于()A.π/3 B.π/6 C.2kπ+π/3(k∈Z) D.2kπ+π/6(k∈Z) 化简 sin(4k-1/4π- α)+cos(4k+1/4π -α)(k∈Z) 化简sin(4k-1/4π- α)+cos(4k+1/4π -α)(k∈Z)