已知-3

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已知-3已知-3已知-31.已知-31.证明:∵-3∴a-b<0,-1<-b<3∴-4<a-b<0∵,-2∴c^2>4∴-162.∵π/-2∴-π/4<β/2≤π/4,-π/4≤-β/2<π/4,-π

已知-3
已知-3

已知-3
1.已知-3

1.证明:∵-3∴a-b<0,-1<-b<3
∴-4<a-b<0
∵,-2∴c^2>4
∴-16<(a-b)*c^2<0
2.∵π/-2<=α<β<=π/2
∴-π/4<β/2≤π/4,-π/4≤-β/2<π/4,-π/2≤α<π/2
∴-3π/4≤α-β/2<3π/4,-3π/4<α+β/2<3π/4

ππ两式相加可知
π<(a+b)/2<2π
由②可知-2π≤-b<-π ③
①+③可得
-π/2<(a-b)/2<π/2