Question

$\cos 10+\cos 110+\cos 130=0$

Answer 1

LHS $\cos 10+\cos 110+\cos 130$

$=2\cos 60\cos 50+\cos 130[\cos C+\cos D=2\cos \frac{C+D}{2}\cos \frac{C-D}{2}]$
$=2\times \frac{1}{2}\cos 50+\cos 130$
$=\cos 50+\cos 130$
$=2\cos 90\cos 40$
$=2\left(0\right)\cos 40$
$=0$