如果θ满足条件sinθ=2k-2/k+6,cosθ=2-k/k+6,则k=
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如果θ满足条件sinθ=2k-2/k+6,cosθ=2-k/k+6,则k=
如果θ满足条件sinθ=2k-2/k+6,cosθ=2-k/k+6,则k=
如果θ满足条件sinθ=2k-2/k+6,cosθ=2-k/k+6,则k=
把sinθ=2k-2/k+6,cosθ=2-k/k+6代入sin²θ+cos²θ=1得
[(2k-2)/(k+6)]²+[(2-k)/(k+6)]²=1
去分母得
(2k-2)²+(2-k)²=(k+6)²
4k²-8k+4+k²-4k+4=k²+12k+36
4k²-24k-28=0
k²-6k-7=0
(k-7)(k+1)=0
k1=7 k2=-1
答案:k=7或-1