If sinx.sin(60°+x).sin(60°−x)=18 then x=

n π 3 + ( − 1 ) n π 18 , n ∈ z

If sinx.sin(60°+x).sin(60°−x)=18 then x=

n π 3 + ( − 1 ) n π 18 , n ∈ z

n π + ( − 1 ) n π 3 , n ∈ z

n π 3 + ( − 1 ) n π 18 , n ∈ z

n π + ( − 1 ) n π 6 , n ∈ z

n π 3 + ( − 1 ) n π 9 , n ∈ z

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If $\sin x . \sin (60 ° + x) . \sin (60 ° - x) = \frac{1}{8}$ then $x =$

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$n π + {(- 1)}^{n} \frac{π}{3}, n \in z$

$\frac{n π}{3} + {(- 1)}^{n} \frac{π}{18}, n \in z$

$n π + {(- 1)}^{n} \frac{π}{6}, n \in z$

$\frac{n π}{3} + {(- 1)}^{n} \frac{π}{9}, n \in z$

answer is B.

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Detailed Solution

$\sin x . \sin (60 ° + x) . \sin (60 ° - x) = \frac{1}{8} \Rightarrow \frac{1}{4} \sin 3 x = \frac{1}{8_{2}} \Rightarrow 3 x = n π + {(- 1)}^{n} \frac{π}{6}, n \in z \Rightarrow x = \frac{n π}{3} + {(- 1)}^{n} \frac{π}{18}, n \in z$

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