Question

已知sinα是方程5x²-7x-6=0的根，求[sin(-α+3π/2)sin(π-α)tan²(2π-α)]

[sin(-α+3π/2)sin(π-α)tan²(2π-α)]/[cos(π-α)cos(π/2+α)tan(π-α)]的值

Answer 1

(x-2)(5x+3)=0
0<=sina<=1
所以sina=-3/5
sin²a=9/25
cos²a=1-sin²a=16/25

原式=(-sina)sinatan²a/[(-cosa)(-sina)(-tana)
=sinatana/cosa
=sin²a/cos²a
=9/16

Answer 2

sinx在(π/6,π/2)递增，(π/2,2π/3)递减
所以x=π/2，y最大=sinπ/2=1

最小在边界
sinπ/6=1/2,sin2π/3=√3/2
所以1/2≤y≤1