2sin^2(x)+10cos^2(x/2)=7-2k,则k?

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2sin^2(x)+10cos^2(x/2)=7-2k,则k?
2sin^2(x)+10cos^2(x/2)=7-2k,则k?

2sin^2(x)+10cos^2(x/2)=7-2k,则k?
2sin²x+10cos²(x/2)=7-2k
2(1-cos²x)+5(1+cosx)=7-2k
2cos²x-5cosx=2k
(cosx -5/4)²=(16k+25)/16
-1≤cosx≤1
1/16≤(cosx-5/4)²≤81/16
要方程有解
1/16≤(16k+25)/16≤81/16
1≤16k+25≤81
-24≤16k≤56
-3/2≤k≤7/2

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