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

As `2cosx, |cosx| and 1-3cos^2x` are in G.P.

`:. |cosx|^2 = 2cosx(1-3cos^2x)`

`=>cos^2x = 2cosx-6cos^3x`

`=>6cos^3x+cos^2x-2cosx = 0`

`=>cosx(6cos^2x+cosx-2) = 0`

`=>cosx(6cos^2x+4cosx-3cosx-2) = 0`

`=>cosx(2cosx-1)(3cosx+2) = 0`

`=>cosx = 0 or 2cosx-1 = 0 or 3cosx+2 = 0`

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