Question

Find the value of $\cos {24}^o+\cos {55}^o+\cos {125}^o+\cos {204}^o+\cos {300}^o$.

Answer 1

Now,

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

$=\cos {24}^o+\cos {55}^o+\cos ({180}^o-{55}^o)+\cos ({180}^o+{24}^o)+\cos (3\times {90}^o+{30}^o)$

$=\cos {24}^o+\cos {55}^o-\cos (-{55}^o)-\cos \left({24}^o\right)+\sin \left({30}^o\right)$

$=\sin {30}^o$

$=\frac{1}{2}$.