Question

$\cos {24}^o+\cos {55}^o+\cos {125}^o+\cos {204}^o+\cos {300}^o=\frac{1}{2}$

Answer 1

It is given that $\cos {24}^{\circ }+\cos {55}^{\circ }+\cos {125}^{\circ }+\cos {204}^{\circ }+\cos {300}^{\circ }=\frac{1}{2}$

As $\cos \left({180}^{\circ }-{55}^{\circ }\right)=-\cos {125}^{\circ }$

$\cos \left({180}^{\circ }+{24}^{\circ }\right)=-\cos {124}^{\circ }$

$\cos \left({360}^{\circ }-{300}^{\circ }\right)=\cos {60}^{\circ }$

Therefore,

$\cos {24}^{\circ }-\cos {125}^{\circ }+\cos {125}^{\circ }-\cos {24}^{\circ }+\cos {60}^{\circ }$

$=\frac{1}{2}$

$=RHS$