The value of

Question:

The value of $\frac{\cos 50^{\circ}}{\cos 130^{\circ}}$ is ______ .

Solution:

$\frac{\cos 50^{\circ}}{\cos 130^{\circ}}=\frac{\cos 50^{\circ}}{\cos \left(180^{\circ}-50^{\circ}\right)}$

$=\frac{\cos 50^{\circ}}{-\cos 50^{\circ}} \quad\left(\because \cos \left(180^{\circ}-\theta\right)=-\cos \theta\right)$

$=-1$

Hence $\frac{\cos 50^{\circ}}{\cos 130^{\circ}}=-1$

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