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  4. If sin (60°-θ), sin θ, sin (60°+θ) (taken in that order) are in G.P., then cos 2 θ is equal to

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Q. If $\sin \left(60^{\circ}-\theta\right), \sin \theta, \sin \left(60^{\circ}+\theta\right)$ (taken in that order) are in G.P., then $\cos ^2 \theta$ is equal to

Sequences and Series

Solution:

We have, $\sin ^2 \theta=\sin ^2 60^{\circ}-\sin ^2 \theta \Rightarrow 2 \sin ^2 \theta=\frac{3}{4} $
$\Rightarrow \sin ^2 \theta=\frac{3}{8}$
$\therefore \cos ^2 \theta=1-\frac{3}{8}=\frac{5}{8} $