Find the value of `cot54^@/(tan36^@)+tan20^@/(cot70^@)`

Explanation

To solve the expression \( \frac{\cot 54^\circ}{\tan 36^\circ} + \frac{\tan 20^\circ}{\cot 70^\circ} \), we can follow these steps:

### Step 1: Rewrite cotangent and tangent functions
We know that:
- \( \cot 54^\circ = \cot(90^\circ - 36^\circ) = \tan 36^\circ \)
- \( \tan 20^\circ = \tan(90^\circ - 70^\circ) = \cot 70^\circ \)

### Step 2: Substitute the identities into the expression
Now, we can substitute these identities into the expression:
\[ \frac{\cot 54^\circ}{\tan 36^\circ} + \frac{\tan 20^\circ}{\cot 70^\circ} = \frac{\tan 36^\circ}{\tan 36^\circ} + \frac{\cot 70^\circ}{\cot 70^\circ} \]

### Step 3: Simplify the fractions
Both fractions simplify to 1:
\[ \frac{\tan 36^\circ}{\tan 36^\circ} = 1 \quad \text{and} \quad \frac{\cot 70^\circ}{\cot 70^\circ} = 1 \]

### Step 4: Add the simplified results
Now, we add the results:
\[ 1 + 1 = 2 \]

### Final Result
Thus, the value of the expression is:
\[ \boxed{2} \]