论文部分内容阅读
题1设x∈(1,2),求证:1/x+1/(2-x)>2.证明设x=2sin2θ(θ∈(π/4,π/2)),则1/x+1(2-x)=1/2csc2θ+1/(2cos2θ)=1/2csc2θ+1/2sec2θ=1/2(1+cot2θ+1+tan2θ)=1/2(2+tan2θ+cot2θ)≥1/2(2+2(tan2θcot2θ)~(1/2)(但等号不成立)
Question 1 Let x∈(1,2) verify that: 1/x+1/(2-x)>2. Proof Let x=2sin2θ(θ∈(π/4,π/2)), then 1/x +1(2-x)=1/2csc2θ+1/(2cos2θ)=1/2csc2θ+1/2sec2θ=1/2(1+cot2θ+1+tan2θ)=1/2(2+tan2θ+cot2θ)≥ 1/2(2+2(tan2θcot2θ)~(1/2) (but the equal sign does not hold)