The value of the expression `(tan^2 20^0-sin^2 20^0)/(tan^2 20^0+sin^2 20^0)` is__________

Explanation

To solve the expression \((\tan^2 20^\circ - \sin^2 20^\circ) / (\tan^2 20^\circ + \sin^2 20^\circ)\), we will follow these steps:

### Step 1: Rewrite \(\tan^2 20^\circ\)
We know that \(\tan^2 \theta = \frac{\sin^2 \theta}{\cos^2 \theta}\). Therefore, we can rewrite \(\tan^2 20^\circ\) as:
\[ \tan^2 20^\circ = \frac{\sin^2 20^\circ}{\cos^2 20^\circ} \]

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