Mathematics - Trigonometric Ratios & Identities Question with Solution | TestHub

$\cos 2A+\cos 2B+\cos 2C=-1-4\cos A\cos B\cos C$. For an acute or right triangle $\cos A\cos B\cos C\le \frac{1}{8}$ (maximum at the equilateral triangle), so the sum is $\ge -\frac{3}{2}$. For an obtuse triangle $\cos A\cos B\cos C<0$, so the sum is $>-1>-\frac{3}{2}$. In every case the sum is $\ge -\frac{3}{2}$.