Question

Решите уравнение: sin^2 x – cos x = 1

Answer 1

Ответ:

$x=\frac{\pi}{2}+\pi k, x = \pi+2\pi n, k,n \in Z$

Пошаговое объяснение:

$\sin^2 x - \cos x = 1;$

$1-\cos^2 x - \cos x = 1;$

$\cos^2 x + \cos x = 0;$

$\cos x(\cos x + 1) = 0;$

$\left [ {{\cos x=0} \atop {\cos x+1=0}} \right. => \left [ {{\cos x=0} \atop {\cos x=-1}} \right. => \left [ {{x=\frac{\pi}{2}+\pi k} \atop {x = \pi + 2\pi n}} \right., k,n \in Z$