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

Options

A. `pi/3`
B. `pi/4`
C. `pi/2`
D. none of these

Answer

D

Explanation

`cos^(2) x=2 cos x(1-3 cos^(2) x)`
or `6 cos^(2) x+ cos^(2) x-2 cos x=0`
or `cos x=0, 1/2, -2/3`
`rArr x=pi/2, pi/3, cos^(-1) (-2/3)" "( :' alpha, beta" are +ve")`
If `alpha =pi/2, beta =pi/3`, then we have `|alpha-beta|=pi/6`.