Value of `(3+cot80^0cot20^0)/(cot80^0+cot20^0)` is equal to (a)`cot20^0` (b) `tan50^0` (c)`cot50^0` (d) `cotsqrt(20^0)`

Explanation

To solve the expression \((3+\cot 80^\circ \cot 20^\circ)/(\cot 80^\circ + \cot 20^\circ)\), we will follow these steps:

### Step 1: Rewrite cotangent in terms of sine and cosine
We know that:
\[ \cot \theta = \frac{\cos \theta}{\sin \theta} \]
Thus, we can rewrite \(\cot 80^\circ\) and \(\cot 20^\circ\):
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