Question

Prove that: cos 24° + cos 55° + cos 125° + cos 204° + cos 300° = \[\frac{1}{2}\]

Answer 1

 LHS =\[ \cos 24^\circ + \cos 55^\circ + \cos 125^\circ + \cos 204^\circ + \cos 300^\circ\]
\[ = \cos 24^\circ + \cos \left( 90^\circ - 35^\circ \right) + \cos \left( 90^\circ e \times 1 + 35^\circ \right) + \cos \left( 90^\circ \times 2 + 24^\circ \right) + \cos \left( 90^\circ \times 3 + 30^\circ \right)\]
\[ = \cos 24^\circ + \sin 35^\circ - \sin 35^\circ e - \cos 24^\circ + \sin 30^\circ \]
\[ = 0 + 0 + \frac{1}{2}\]
\[ = \frac{1}{2}\]
= RHS
Hence proved .