设θ是三角形的最小内角,且acos²θ2+sin²θ2-cos²θ2-asin²θ2=a+1,则a的取值范

宝宝妈妈2023-04-27  42

cos²θ/2-sin²θ/2=cosθ

所以(a-1)cosθ=a+1

cosθ=(a+1)/(a-1)

θ是三角形的最小内角

所以0<θ<=60度

1/2<=cosθ<1

1/2<=(a+1)/(a-1)

(a+1)/(a-1)-1/2>=0

(2a+2-a+1)/(a-1)>=0

所以(a+3)(a-1)>=0

a<=-3,a>1

(a+1)/(a-1)<1

(a+1)/(a-1)-1<0

2/(a-1)<0

a<1

所以a<=-3


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