Prove that `(4 cos^(2)9^(@)-3)(4 cos ^(2)27^(@)-3)=tan 9^(@)`.

Explanation

To prove that \( (4 \cos^2 9^\circ - 3)(4 \cos^2 27^\circ - 3) = \tan 9^\circ \), we will start with the left-hand side (LHS) and simplify it step by step.

### Step 1: Rewrite the expression using the cosine triple angle formula
We know that:
\[ \cos 3\theta = 4 \cos^3 \theta - 3 \cos \theta \]
From this, we can express \( 4 \cos^2 \theta - 3 \) as:
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