If are in G.P. then is equal to

JEE MainMathematicsModerateSequences and Series

If $\frac{1}{6}sin\theta,cos\theta,tan\theta$ are in G.P. then
$\theta$ is equal to $(n \in Z)$

Show answer and solution

\cos^{2}\theta = \frac{1}{6}sin\theta.tan\theta

6\cos^{3}\theta = 1 - \cos^{2}\theta

6\cos^{3}\theta + \cos^{2}\theta - 1 = 0

(2cos\theta - 1)(3\cos^{2}\theta + 2cos\theta + 1) = 0

cos\theta = \frac{1}{2} \Rightarrow \theta = 2n\pi \pm \frac{\pi}{3},n \in Z

Source: Grass-G / M-16 Mathematics Paper 25 Nov First.docx

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