Question

2sin ^2x-3cosx-3=0

Решите уравнение, пожалуйста!

Answer 1

$2sin^2x-3cosx-3=0\\ 2(1-cos^2x)-3cosx-3=0\\ 2-2cos^2x-3cosx-3=0\\ -2+2cos^2x+3cosx+3=0\\ 2cos^2x+3cosx+1=0\\ t=cos x, t \in [-1;1]$

$2t^2+3t+1=0\\ \left[\begin{gathered} t=-\frac{1}{2}\\ t=-1 \end{gathered} \right.\\ \left[\begin{gathered} cos x=-\frac{1}{2}\\ cos x=-1 \end{gathered} \right.\\ \left[\begin{gathered} x=\pm \frac{2\pi}{3}+2\pi k, k \in Z\\x=\pi+2\pi n, n \in Z \end{gathered} \right.$