Question

Let $\alpha ,\beta$ be any two positive values of $x$ for which $2\cos x,|\cos x|and1-3{\cos }^{2}x$ are in G. PThe minimum value of $|\alpha -\beta |$ is

• A. $\frac{\pi }{3}$
• B. $\frac{\pi }{4}$
• C. $\frac{\pi }{2}$
• D. $\frac{\pi }{6}$

Answer 1

The correct option is D $\frac{\pi }{6}$

${\cos }^{2}x=2\cos x(1-3{\cos }^{2}x)$
$\cos x=0$ or $\cos x=2-6{\cos }^{2}x$
$\cos x=0$ or $6{\cos }^{2}x+\cos x-2=0$
$\cos x=0$ or $\cos x=1/2$
clearly minimum value is $\frac{\Pi }{6}$