Question:
If $\operatorname{Cos} X=\frac{-1}{2}$, find the value of $\cos 3 x$
Solution:
Given: $\operatorname{Cos} X=\frac{-1}{2}$
To find: $\cos 3 x$
We know that,
$\cos 3 x=4 \cos ^{3} x-3 \cos x$
Putting the values, we get
$\cos 3 x=4 \times\left(-\frac{1}{2}\right)^{3}-3 \times\left(-\frac{1}{2}\right)$
$\cos 3 x=4 \times\left(-\frac{1}{8}\right)+\frac{3}{2}$
$\cos 3 x=\left[-\frac{1}{2}+\frac{3}{2}\right]$
$\cos 3 x=\left[\frac{-1+3}{2}\right]$
$\cos 3 x=\frac{2}{2}$
$\cos 3 x=1$
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