Let `alphaa n dbeta` be any two positive values of `x` for which `2cosx ,|cosx|,` and `1-3cos^2x` are in G.P. The minimum value of `|alpha-beta|` is `pi/3` (b) `pi/4` (c) `pi/2` (d) none of these

Explanation

To solve the problem, we need to determine the values of \( x \) for which \( 2\cos x \), \( |\cos x| \), and \( 1 - 3\cos^2 x \) are in geometric progression (G.P.).

### Step 1: Set up the condition for G.P.
For three numbers \( a \), \( b \), and \( c \) to be in G.P., the condition is:
\[ b^2 = ac \]
In our case, let:
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