作业帮已知sinα是方程5x^2-7x-6=0的根α是第三象限,则｛[sin(α-3/2π）cos（3/2π-α）]/[cos(π/2-α)sin(π/2+α)]｝×tan^2(π-α)=｛[sin(α-3/2π）cos（3/2π-α）]为分子，cos(π/2-α)sin(π/2+α)]为分母，与tan^2(π-α)相乘
来源：学生作业帮助网 编辑：作业帮 时间：2024/06/11 00:55:52
![已知sinα是方程5x^2-7x-6=0的根α是第三象限,则｛[sin(α-3/2π）cos（3/2π-α）]/[cos(π/2-α)sin(π/2+α)]｝×tan^2(π-α)=｛[sin(α-3/2π）cos（3/2π-α）]为分子，cos(π/2-α)sin(π/2+α)]为分母，与tan^2(π-α)相乘](/uploads/image/z/1614446-62-6.jpg?t=%E5%B7%B2%E7%9F%A5sin%CE%B1%E6%98%AF%E6%96%B9%E7%A8%8B5x%5E2-7x-6%3D0%E7%9A%84%E6%A0%B9%CE%B1%E6%98%AF%E7%AC%AC%E4%B8%89%E8%B1%A1%E9%99%90%2C%E5%88%99%EF%BD%9B%5Bsin%28%CE%B1-3%2F2%CF%80%EF%BC%89cos%EF%BC%883%2F2%CF%80-%CE%B1%EF%BC%89%5D%2F%5Bcos%28%CF%80%2F2-%CE%B1%29sin%28%CF%80%2F2%2B%CE%B1%29%5D%EF%BD%9D%C3%97tan%5E2%28%CF%80-%CE%B1%29%3D%EF%BD%9B%5Bsin%28%CE%B1-3%2F2%CF%80%EF%BC%89cos%EF%BC%883%2F2%CF%80-%CE%B1%EF%BC%89%5D%E4%B8%BA%E5%88%86%E5%AD%90%EF%BC%8Ccos%28%CF%80%2F2-%CE%B1%29sin%28%CF%80%2F2%2B%CE%B1%29%5D%E4%B8%BA%E5%88%86%E6%AF%8D%EF%BC%8C%E4%B8%8Etan%5E2%28%CF%80-%CE%B1%29%E7%9B%B8%E4%B9%98)
已知sinα是方程5x^2-7x-6=0的根α是第三象限,则｛[sin(α-3/2π）cos（3/2π-α）]/[cos(π/2-α)sin(π/2+α)]｝×tan^2(π-α)=｛[sin(α-3/2π）cos（3/2π-α）]为分子，cos(π/2-α)sin(π/2+α)]为分母，与tan^2(π-α)相乘
已知sinα是方程5x^2-7x-6=0的根α是第三象限,则｛[sin(α-3/2π）cos（3/2π-α）]/[cos(π/2-α)sin(π/2+α)]｝×tan^2(π-α)=
｛[sin(α-3/2π）cos（3/2π-α）]为分子，cos(π/2-α)sin(π/2+α)]为分母，与tan^2(π-α)相乘
已知sinα是方程5x^2-7x-6=0的根α是第三象限,则｛[sin(α-3/2π）cos（3/2π-α）]/[cos(π/2-α)sin(π/2+α)]｝×tan^2(π-α)=｛[sin(α-3/2π）cos（3/2π-α）]为分子，cos(π/2-α)sin(π/2+α)]为分母，与tan^2(π-α)相乘
｛[sin(α-3/2π）cos（3/2π-α）]/[cos(π/2-α)sin(π/2+α)]｝×tan^2(π-α)
=｛-sin(3/2π-a)cos（3/2π-α）]/[cos(π/2-α)sin(π/2+α)]｝×tan^2(π-α)
=｛-1/2sin(3π-2a)]/[cos(π/2-α)sin(π/2+α)]｝×tan²α
=｛-1/2sin2a]/[sinacosa]｝tan²α
=｛-sin2a]/[2sinacosa]｝tan²α
=-tan²α
5x^2-7x-6=0
1 -2
5 3
(x-2)(5x+3)=0
sina=-3/5
cosa=-4/5
tana=3/4
tan²a=9/16
∴-9/16