Question

Find the value of $\cos \left({306}^o\right)+\cos \left({234}^o\right)+\cos \left({162}^o\right)+\cos {18}^o$.

Answer 1

We have,

$\cos \left({306}^o\right)+\cos \left({234}^o\right)+\cos \left({162}^o\right)+\cos {18}^o$

$=\cos (3\times {90}^o+{36}^o)+\cos (3\times {90}^o-{36}^o)+\cos (2\times {90}^o-{18}^o)+\cos {18}^o$

$=\cos \left({36}^o\right)-\cos \left({36}^o\right)-\cos \left({18}^o\right)+\cos {18}^o$

$=0$.