Решите уравнение \({\cos^2\left(\dfrac{x}{2}+\dfrac{\pi}{3}\right)-1=0.}\) Выберите вариант ответа. \({-\dfrac{2\pi}{3}+4{\pi}n,n\in{\mathbf{Z}};\dfrac{4\pi}{3}+4{\pi}k,k\in{\mathbf{Z}}}\) \({-\dfrac{2\pi}{3}+2{\pi}n,n\in{\mathbf{Z}};\dfrac{4\pi}{3}+2{\pi}k,k\in{\mathbf{Z}}}\) \({-\dfrac{\pi}{3}+2{\pi}n,n\in{\mathbf{Z}};\dfrac{2\pi}{3}+2{\pi}k,k\in{\mathbf{Z}}}\) \({\pm{\pi}-\dfrac{\pi}{3}+4{\pi}n,n\in{\mathbf{Z}}}\)

Задание

Решите уравнение \({\cos^2\left(\dfrac{x}{2}+\dfrac{\pi}{3}\right)-1=0.}\) Выберите вариант ответа.

\({-\dfrac{2\pi}{3}+4{\pi}n,n\in{\mathbf{Z}};\dfrac{4\pi}{3}+4{\pi}k,k\in{\mathbf{Z}}}\)
\({-\dfrac{2\pi}{3}+2{\pi}n,n\in{\mathbf{Z}};\dfrac{4\pi}{3}+2{\pi}k,k\in{\mathbf{Z}}}\)
\({-\dfrac{\pi}{3}+2{\pi}n,n\in{\mathbf{Z}};\dfrac{2\pi}{3}+2{\pi}k,k\in{\mathbf{Z}}}\)
\({\pm{\pi}-\dfrac{\pi}{3}+4{\pi}n,n\in{\mathbf{Z}}}\)