Question

Prove that :

\[ \cos24^\circ+\cos55^\circ+\cos125^\circ+\cos204^\circ+\cos300^\circ=\frac12 \]

Solution

\[ \begin{aligned} &\cos24^\circ+\cos55^\circ+\cos125^\circ+\cos204^\circ+\cos300^\circ \\[4pt] =& \cos24^\circ+\cos55^\circ-\cos55^\circ-\cos24^\circ+\cos60^\circ \\[4pt] =& \frac12 \end{aligned} \]

Using,

\[ \cos(180^\circ-\theta)=-\cos\theta, \qquad \cos(180^\circ+\theta)=-\cos\theta \]

Hence Proved.