Question

若sinθ=(m-3)/(m+5),cosθ=(4-2m)/(m+5), θ∈(π/2, π), 则m= ? , tanθ = ?

要解题过程，谢谢！

Answer 1

sin²θ+cos²θ=1
[(m-3)/(m+5)]²+[(4-2m)/(m+5)]²=1
(m-3)²+(4-2m)²=(m+5)²
m²-6m+9+16-16m+4m²=m²+10m+25
4m²-32m-0
m=0或m=8
(1) m=0 ，sinθ=-3/5 与θ∈(π/2, π), 矛盾
(2)m=8
siinθ=5/13,cosθ=-12/13

所以 m=8,tan θ=sinθ/cosθ= -5/12

追问

sinθ=-3/5 与θ∈(π/2, π),为什么矛盾

追答

θ∈(π/2, π),
sinθ>0
所以矛盾