Question:
If $\operatorname{Sin} X=\frac{1}{6}$, find the value of $\sin 3 x$
Solution:
$\operatorname{Sin} X=\frac{1}{6}$
Given: $\operatorname{Sin} X=\frac{1}{6}$
To find: $\sin 3 x$
We know that,
$\sin 3 x=3 \sin x-\sin ^{3} x$
Putting the values, we get
$\sin 3 x=3 \times\left(\frac{1}{6}\right)-\left(\frac{1}{6}\right)^{3}$
$\sin 3 x=\frac{1}{6}\left[3-\left(\frac{1}{6}\right)^{2}\right]$
$\sin 3 x=\frac{1}{6}\left[3-\frac{1}{36}\right]$
$\sin 3 x=\frac{1}{6}\left[\frac{108-1}{36}\right]$
$\sin 3 x=\frac{107}{216}$
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