Question

If $\frac{1}{6}\sin \theta ,\cos \theta$ and $\tan \theta$ are in GP, then the general value of $\theta$ is

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

${\cos }^2\theta =\frac{1}{6}\sin \theta .$ Tan $\theta$ or $6{\cos }^3\theta +{\cos }^2\theta -1=0$
As, $\cos \theta =\frac{1}{2}$ satisfies the euation (by trial)
$(2\cos \theta -1)(3{\cos }^2\theta +2\cos \theta +1)=0$
$\Rightarrow \cos \theta =\frac{1}{2}$ (other values of cos $\theta$ are imaginary)
So, $\theta =2n\pi \pm \frac{\pi }{3},$