Evaluate :
`(cot^(2)41^(@))/(tan^(2)49^(@))-2(sin^(2)75^(@))/(cos^(2)15^(@))`

Answer

To evaluate the expression

\[ \frac{\cot^2 41^\circ}{\tan^2 49^\circ} - 2 \frac{\sin^2 75^\circ}{\cos^2 15^\circ} \]

we will use the properties of complementary angles.

### Step-by-Step Solution:

1. **Recognize Complementary Angles:**
We know that \( \tan(90^\circ - \theta) = \cot(\theta) \) and \( \sin(90^\circ - \theta) = \cos(\theta) \).

2. **Rewrite the First Term:**
We can rewrite \( \cot^2 41^\circ \) as:
\[ \cot^2 41^\circ = \cot^2(90^\circ - 49^\circ) = \tan^2 49^\circ \]
Therefore, the first term becomes:
\[ \frac{\cot^2 41^\circ}{\tan^2 49^\circ} = \frac{\tan^2 49^\circ}{\tan^2 49^\circ} = 1 \]

3. **Rewrite the Second Term:**
For the second term, we can rewrite \( \sin^2 75^\circ \) as:
\[ \sin^2 75^\circ = \sin^2(90^\circ - 15^\circ) = \cos^2 15^\circ \]
Thus, the second term becomes:
\[ 2 \frac{\sin^2 75^\circ}{\cos^2 15^\circ} = 2 \frac{\cos^2 15^\circ}{\cos^2 15^\circ} = 2 \]

4. **Combine the Results:**
Now substituting back into the original expression, we have:
\[ 1 - 2 = -1 \]

### Final Answer:
Thus, the value of the expression is:
\[ \boxed{-1} \]