The number of solutions of $sin x + sin 3 x + sin 5 x = 0$ in the interval $[\frac{π}{2}, 3 \frac{π}{2}]$ is

2

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3

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4

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5

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Solution

The correct option is A $3$
GIven equation is $s i n x + s i n 3 x + s i n 5 x = 0$ ,
$⟹ s i n x + s i n 5 x = - s i n 3 x$
$⟹ 2 s i n 3 x c o s 2 x = - s i n 3 x$
$⟹ s i n 3 x (2 c o s 2 x + 1) = 0$
$⟹ s i n 3 x = 0 o r c o s 2 x = \frac{- 1}{2}$ $⟹ x = \frac{2 π}{3}, π, \frac{4 π}{3} o r x = \frac{2 π}{3}, \frac{4 π}{3}$

The number of common solutions in the given interval are $3$ .

Suggest Corrections

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