Question

помогите решить
2cos^2 x=1

Answer 1

Ответ:

$\frac{\pi }{4} +\frac{\pi n }{2} ,~n\in\mathbb {Z}$

Объяснение:

$2cos^{2} x=1;\\2cos^{2} x-1=0;\\2cos^{2} x- ( sin^{2} x+cos^{2} x)=0;\\2cos^{2} x- sin^{2} x-cos^{2} x=0\\cos^{2} x-sin^{2} x=0;\\cos2x=0;\\\\2x=\frac{\pi }{2} +\pi n, ~n\in\mathbb {Z};\\\\x= \frac{\pi }{4} +\frac{\pi n }{2} ,~n\in\mathbb {Z}$