Question

решите уравнение 2cos^2 x = 1​

Answer 1

$2\cos^2 x = 1$

$\cos^2 x = \dfrac{1}{2}$

$\cos x =\pm \sqrt{\dfrac{1}{2} }$

$\left[\begin{array}{l}\cos x ={\dfrac{\sqrt{2} }{2}\\\cos x =-{\dfrac{\sqrt{2} }{2}\end{array}\right$

$\left[\begin{array}{l}x=\pm\dfrac{\pi}{4} +2\pi n\\ x=\pm\dfrac{3\pi}{4} +2\pi n\end{array}\right$

$\boxed{x=\dfrac{\pi }{4} +\dfrac{\pi n}{2} ,\ n\in\mathbb{Z}}$