If $sin x, sin 2 x, sin 3 x$ are in $A . P$ then $x =$

n π, n \in l

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n x, n \in l

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2 n π, n \in l

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(2 n + 1) π, n \in l

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Solution

The correct option is C $2 n π, n \in l$
$sin x, sin 2 x, sin 3 x$ are in $A . P .$
Hence,
$2 sin 2 x = sin x + sin 3 x = 2 sin 2 x cos x$
or
$2 sin 2 x (1 - cos x) = 0$
or if either $sin 2 x = 0 o r cos x = 1$
which is satisfied by $x = 2 n π$ for which $cos x = 1$ .
correct answer is $(c) x = 2 n π, n \in I$

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