Question

The value of $\frac{\cos 50°}{\cos 130°}$ is _____________.

Answer 1

$\begin{array}{rcl}\frac{\cos 50°}{\cos 130°}& =& \frac{\cos 50°}{\cos \left(180°-50°\right)}\\ & =& \frac{\cos 50°}{-\cos 50°}\left(\because \cos \left(180°-\theta \right)=-\cos \theta \right)\\ & =& -1\end{array}$
$\mathrm{Hence}\frac{\cos 50°}{\cos 130°}=-1$