Evaluate `2(cos^(2)28^(@)-sin^(2)62^(@))`.

Answer

To evaluate the expression \( 2(\cos^2 28^\circ - \sin^2 62^\circ) \), we can follow these steps:

### Step 1: Rewrite the expression
We start with the expression:
\[ 2(\cos^2 28^\circ - \sin^2 62^\circ) \]

### Step 2: Use the co-function identity
We know from trigonometric identities that:
\[ \sin(90^\circ - \theta) = \cos(\theta) \]
Thus, we can express \(\sin 62^\circ\) in terms of cosine:
\[ \sin 62^\circ = \cos(90^\circ - 62^\circ) = \cos 28^\circ \]

### Step 3: Substitute the identity into the expression
Now, we can substitute \(\sin^2 62^\circ\) with \(\cos^2 28^\circ\):
\[ 2(\cos^2 28^\circ - \cos^2 28^\circ) \]

### Step 4: Simplify the expression
Now we can simplify the expression:
\[ 2(0) = 0 \]

### Final Answer
Thus, the value of \( 2(\cos^2 28^\circ - \sin^2 62^\circ) \) is:
\[ \boxed{0} \]