这里给出杨乐不等式则与目前已见到的证明不同的两个初等证明．证明1（三角变换法）汪意到余弦函数在[0，π]上是减函数，有又由A＞0，B＞0，A＋B≤π知|A－B|＜π，从而有COSμ（A-B）=COSμ|A-B|＞COSμπ由①②③即知（*）成立．证明2（构造模型法）当μ=1时易知（*）成立； Here we show two elementary proofs that Yang Le inequality is different from the proofs that have been seen so far. Prove that 1 (triangular transformation method) Wang Yi to cosine function is a decreasing function on [0, π], there is again by A> 0, B> 0, A + B ≤ π known | A-B | <π, thus there COSμ ( AB)=COSμ|AB|>COSμπ is established by 123 (*). Proof 2 (structural model method) is easy to know (*) when μ=1;