Question

若sinθ＝m－3/m＋5,cosθ＝4－5m/m＋5,且θ为第二象限角,求m的值

Answer 1

sin²θ+cos²θ=1

[(m-3)/(m+5)]²+[(4-5m)/(m+5)]²=1

(m-3)²+(4-5m)²=(m+5)²

m²-6m+9+16-40m+25m²=m²+10m+25

25m²-56m=0

m=0或m=56/25

(1) 当m=0 ,sinθ=-3/5 与θ∈(π/2, π), 矛盾,舍去

(2)m=56/25

sinθ>0,cosθ