8.062. $\cos ^{3} x+\cos ^{2} x-4 \cos ^{2} \frac{x}{2}=0$.

8.062. $\cos ^{3} x+\cos ^{2} x-4 \cos ^{2} \frac{x}{2}=0$.
## Solution.

From the condition

$$
\cos ^{3} x+\cos ^{2} x-4 \cdot \frac{1}{2}(1+\cos x)=0, \cos ^{3} x+\cos ^{2} x-2 \cos x-2=0, \Leftrightarrow
$$

$\Leftrightarrow \cos ^{2} x(\cos x+1)-2(\cos x+1)=0, \Leftrightarrow(\cos x+1)\left(\cos ^{2} x-2\right)=0$.

Then $\cos x+1=0, \cos x=-1, x_{1}=\pi+2 \pi n=\pi(2 n+1), n \in Z ; \cos ^{2} x-2 \neq 0$.

Answer: $\quad x=\pi(2 n+1), \quad n \in Z$.