Question

Find the value of $\cos 24^{\circ }+\cos 5^{\circ }+\cos 175^{\circ }+\cos 204^{\circ }+\cos 300^{\circ }$

Answer 1

Answer: 0.50

$\cos 24^{\circ }+\cos 5^{\circ }+\cos \left(180^{\circ }-5^{\circ }\right)+\cos \left(180^{\circ }+24^{\circ }\right)+\cos \left(360^{\circ }-60^{\circ }\right)$
$=\cos 24^{\circ }+\cos 5^{\circ }-\cos 5^{\circ }-\cos 24^{\circ }+\cos 60^{\circ }$
$=1/2$