Question

The value of $\cos {24}^{\circ }+\cos {55}^{\circ }+\cos {125}^{\circ }+\cos {204}^{\circ }+\cos {300}^{\circ }$ is

• A. $1$
• B. $\frac{1}{2}$
• C. $\frac{1}{3}$
• D. $\frac{1}{4}$

Answer 1

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

$\cos {24}^o+\cos {55}^o+\cos {125}^o+\cos {204}^o+\cos {300}^o$

$\Rightarrow \cos {24}^o+\cos {55}^o+\cos (180-{55}^o)+\cos (180+{24}^o)+\cos (270+{30}^o)$

$\Rightarrow \cos {24}^o+\cos {55}^o-\cos {55}^o-\cos {24}^o+\sin {30}^o$

$\Rightarrow \sin {30}^o$ $\because \sin {30}^o=\frac{1}{2}$

$\Rightarrow \frac{1}{2}$