Question

Solve : $\cos {27}^o+\cos {93}^o+\cos {147}^o$

Answer 1

$\cos {27}^o+\cos {93}^o+\cos {147}^o$

$\Rightarrow 2\cos \left(\frac{{27}^o+93}{2}\right)\cos \left(\frac{27-93}{2}\right)+\cos {147}^o$

$\Rightarrow \cos C+\cos D=2\cos \left(\frac{C+D}{2}\right)\cos \left(\frac{C-D}{2}\right)⟶\left(1\right)$

$\Rightarrow 2\cos \left({60}^o\right)\cos \left({33}^o\right)+\cos {147}^o$

$\because \cos {60}^o=\frac{1}{2}$

$\Rightarrow \cos {33}^o+\cos {147}^o$

Again, using $1$

$\Rightarrow 2\cos \left(\frac{33+147}{2}\right)\cos \left(\frac{33-147}{2}\right)$

$\Rightarrow 2\cos \left({90}^o\right)\cos (-{57}^o)$

$=0$