Prove that:
`cos^(2)48^(@)-sin^(2)12^(@)=(sqrt(5)+1)/(8)`

Explanation

To prove that \( \cos^2 48^\circ - \sin^2 12^\circ = \frac{\sqrt{5} + 1}{8} \), we can use trigonometric identities. Let's go through the proof step by step.

### Step 1: Use the identity for difference of squares
We know that:
\[ \cos^2 A - \sin^2 B = \cos(A + B) \cos(A - B) \]
In our case, let \( A = 48^\circ \) and \( B = 12^\circ \).
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