作业帮已知sinα是方程5x²-7x-6=o的根,求[sin(α+ 3π/2 )sin(3π/2 -α)tan²(2π-α)tan(π-α)] / [cos(π/2 -α)cos(π/2 +α)]的值
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![已知sinα是方程5x²-7x-6=o的根,求[sin(α+ 3π/2 )sin(3π/2 -α)tan²(2π-α)tan(π-α)] / [cos(π/2 -α)cos(π/2 +α)]的值](/uploads/image/z/978307-43-7.jpg?t=%E5%B7%B2%E7%9F%A5sin%CE%B1%E6%98%AF%E6%96%B9%E7%A8%8B5x%26%23178%3B-7x-6%3Do%E7%9A%84%E6%A0%B9%2C%E6%B1%82%5Bsin%28%CE%B1%2B+3%CF%80%2F2+%29sin%283%CF%80%2F2+-%CE%B1%29tan%26%23178%3B%282%CF%80-%CE%B1%29tan%28%CF%80-%CE%B1%29%5D+%2F+%5Bcos%28%CF%80%2F2+-%CE%B1%29cos%28%CF%80%2F2+%2B%CE%B1%29%5D%E7%9A%84%E5%80%BC)
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已知sinα是方程5x²-7x-6=o的根,求[sin(α+ 3π/2 )sin(3π/2 -α)tan²(2π-α)tan(π-α)] / [cos(π/2 -α)cos(π/2 +α)]的值
已知sinα是方程5x²-7x-6=o的根,
求[sin(α+ 3π/2 )sin(3π/2 -α)tan²(2π-α)tan(π-α)] / [cos(π/2 -α)cos(π/2 +α)]的值
已知sinα是方程5x²-7x-6=o的根,求[sin(α+ 3π/2 )sin(3π/2 -α)tan²(2π-α)tan(π-α)] / [cos(π/2 -α)cos(π/2 +α)]的值
sin(α+ 3π/2 )=-cosα
sin(3π/2 -α)=-cosα
tan(2π-α)=-tanα
tan(π-α)=-tanα
cos(π/2-α)=sinα
cos(π/2+α)=-sinα
原式=
[(cosα)^2*(-tanα)^3]/[-(sinα)^2]
=[(cosα)^2*(tanα)^3]/[(sinα)^2]
=tanα
5x²-7x-6=0
(5x+3)(x-2)=0
∵sinα∈[-1,1]
∴sinα=-3/5
cosα=±4/5
tanα=±3/4
答：原式=±3/4