三角函数恒等式

hbghlyj

证明恒等式：\begin{multline}\frac{\cos4A}{\sin A\sin(A-B)\sin(A-C)}\\+\frac{\cos4B}{\sin B\sin(B-A)\sin(B-C)}\\+\frac{\cos4C}{\sin C\sin(C-A)\sin(C-B)}\\=8\sin(A+B+C)+\csc A\csc B\csc C\end{multline}
wolframalpha.com/input?i=%28cos%284*A%29%2F%28sin%28A%29*sin%28A ... 28B%29*csc%28C%29%29

ZCos666

等价于恒等式
\[ \sum\dfrac{(x^8+1)yz}{x(x^2-1)(x^2-y^2)(x^2-z^2)}=xyz-\dfrac{1}{xyz}+\dfrac{2xyz}{(x^2-1)(y^2-1)(z^2-1)} \]

hbghlyj

可以推广吗