Question

\[ \frac{\cos50^\circ}{\cos130^\circ} \]

Solution

Using identity

\[ \cos(180^\circ-\theta)=-\cos\theta \]

\[ \cos130^\circ = \cos(180^\circ-50^\circ) \]

\[ =-\cos50^\circ \]

Therefore,

\[ \frac{\cos50^\circ}{\cos130^\circ} = \frac{\cos50^\circ}{-\cos50^\circ} =-1 \]

Answer

\[ \boxed{-1} \]