<s>[INST] If $\frac{\sin^2 A + \sin^2 B + \sin^2 C}{\cos^2 A + \cos^2 B + \cos^2 C}=2$ , then $\triangle ABC$ is a right triangle 
Show that the triangle whose angles satisfy the equality
  $$\frac{\sin^2 A + \sin^2 B + \sin^2 C}{\cos^2 A + \cos^2 B + \cos^2 C}=2$$
  is right-angled.

I've tried many times, but was unsuccessful.
 [/INST] Hint: Show that 
\begin{eqnarray*}
1-\cos^2 A-\cos^2 B-\cos^2C+ 2\cos A \cos B \cos C =0
\end{eqnarray*}
for any triangle.
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