Evaluate:
`((cos 47^(@))/(sin 43^(@)))^(2)+((sin72^(2))/(cos 18^(@)))^(2)-2cos^(2)45^(@)`

Answer

To evaluate the expression

\[ \left(\frac{\cos 47^\circ}{\sin 43^\circ}\right)^2 + \left(\frac{\sin 72^\circ}{\cos 18^\circ}\right)^2 - 2\cos^2 45^\circ, \]

we will follow these steps:

### Step 1: Use Complementary Angle Identities
We know that:
- \(\sin(90^\circ - x) = \cos x\)
- \(\cos(90^\circ - x) = \sin x\)

Using these identities, we can rewrite \(\sin 43^\circ\) and \(\cos 18^\circ\):
- \(\sin 43^\circ = \cos(90^\circ - 43^\circ) = \cos 47^\circ\)
- \(\cos 18^\circ = \sin(90^\circ - 18^\circ) = \sin 72^\circ\)

### Step 2: Substitute the Identities
Now we can substitute these identities into the expression:

\[ \left(\frac{\cos 47^\circ}{\cos 47^\circ}\right)^2 + \left(\frac{\sin 72^\circ}{\sin 72^\circ}\right)^2 - 2\cos^2 45^\circ \]

### Step 3: Simplify the Expression
This simplifies to:

\[ 1^2 + 1^2 - 2\cos^2 45^\circ \]

### Step 4: Calculate \(\cos^2 45^\circ\)
We know that:

\[ \cos 45^\circ = \frac{1}{\sqrt{2}} \]

Thus,

\[ \cos^2 45^\circ = \left(\frac{1}{\sqrt{2}}\right)^2 = \frac{1}{2} \]

### Step 5: Substitute \(\cos^2 45^\circ\) into the Expression
Now substituting this back into our expression gives:

\[ 1 + 1 - 2 \times \frac{1}{2} \]

### Step 6: Final Calculation
This simplifies to:

\[ 1 + 1 - 1 = 1 \]

Thus, the final answer is:

\[ \boxed{1} \]