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
问题描述：
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
答
sin(α+ 3π/2 )=-cosαsin(3π/2 -α)=-cosαtan(2π-α)=-tanαtan(π-α)=-tanαcos(π/2-α)=sinαcos(π/2+α)=-sinα原式=[(cosα)^2*(-tanα)^3]/[-(sinα)^2]=[(cosα)^2*(tanα)^3]/[(sinα)^2]=tanα5x...