Solve this


If $\operatorname{Cos} X=\frac{-1}{2}$, find the value of $\cos 3 x$



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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