Question

$\cos {24}^0+\cos 5^0+\cos {175}^0+\cos {204}^0+\cos {300}^0=$

• A. $\frac{1}{2}$
• B. $\frac{-1}{2}$
• C. $\frac{\sqrt{3}}{2}$
• D. $1$

Answer 1

The correct option is A $\frac{1}{2}$

We know that,

$\cos {175}^{\circ }=\cos (180-5{)}^{\circ }=-\cos 5^{\circ }\cos {204}^{\circ }=\cos (180+24{)}^{\circ }=-\cos {24}^{\circ }\cos {300}^{\circ }=\cos (270+30{)}^{\circ }=\sin {30}^{\circ }$

$\Rightarrow$ $\cos {24}^{\circ }+\cos 5^{\circ }+\cos {175}^{\circ }+\cos {204}^{\circ }+\cos {300}^{\circ }$

$=\cos {24}^{\circ }+\cos 5^{\circ }-\cos {24}^{\circ }-\cos 5^{\circ }+\sin {30}^{\circ }$

$=\sin {30}^{\circ }=1/2$