Question

$\cos {55}^0+\cos {65}^0+\cos {175}^0=$

Answer 1

L.H.S. $=\cos {55}^0+\cos {65}^0+\cos {175}^0$
$=2\cos \frac{{55}^0+{65}^0}{2}+\cos \frac{{55}^0-{65}^0}{2}+\cos {175}^0$
$=2\cos {60}^0\cos (-5^0)+\cos {175}^0=2\times \frac{1}{2}\cos 5^0+\cos ({180}^0-5^0)=\cos 5^0-\cos 5^0=0$
Ans: 0