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  4. If sin θ, sin 2 θ, 1 are the first 3 terms of an A.P., then the number of values of θ in (-π, π), is

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Q. If $\sin \theta, \sin ^2 \theta, 1$ are the first 3 terms of an A.P., then the number of values of $\theta$ in $(-\pi, \pi)$, is

Sequences and Series

Solution:

$ \sin \theta, \sin ^2 \theta, 1 \rightarrow \text { A.P. } $
$2 \sin ^2 \theta=1+\sin \theta$
$\sin \theta=1 \text { or } \sin \theta=-\frac{1}{2} $
$\theta=\frac{\pi}{2} \text { or } \theta=\frac{-\pi}{6} \text { or } \theta=\frac{-5 \pi}{6}
$
Hence number of values of $\theta$ are 3 .