Sometimes, its better to adopt a complex way than a simpler one
Geometry
Level
5
\[\sin(x)+\sin(y)+\sin(z)=0 \\ \cos(x)+\cos(y)+\cos(z)=0\]
Given that \(x,y,z\) are real numbers satisfying above two equations , evaluate:
\[\begin{align} &\tan^2(x)+\tan^2(y)+\tan^2(z) \\ - &\tan^2(x)\tan^2(y)-\tan^2(y)\tan^2(z)-\tan^2(x)\tan^2(z) \\ -&3\tan^2(x)\tan^2(y)\tan^2(z) = \ ? \end{align}\]
This problem is original.
by
Nihar Mahajan