Value of $ \cos 52^{\circ} + \cos 68^{\circ} + \cos 172^{\circ} $? I am a little weak in trigonometry. I have two questions:


*

*Find the value of $\cos 52^{\circ} + \cos 68^{\circ} + \cos 172^{\circ} $

*Find the value of $\sin 28^{\circ}+ \cos 17^{\circ} + \cos 28^{\circ} + \sin 17^{\circ} $
I am asking these questions because:
1. I am weak and unable to solve these.
2. I want to know the difference in these questions. 

Note that,
$$
\cos(\alpha\pm \beta)=\cos \alpha\cos \beta\mp\sin \alpha\sin \beta
$$
and
$$
\cos(180^\circ-\alpha)=-\cos\alpha.
$$
Hence
$$
\begin{align}
\cos52^\circ+\cos68^\circ+\cos172^\circ&=\color{blue}{\cos(60^\circ-8^\circ)+\cos(60^\circ+8^\circ)}+\color{red}{\cos(180^\circ-8^\circ)}\\
&=\color{blue}{2\cos60^\circ\cos8^\circ}+(\color{red}{-\cos8^\circ})\\
&=\color{blue}{2\cdot\frac12\cdot\cos8^\circ}-\color{red}{\cos8^\circ}\\
&=0.
\end{align}
$$
