Question

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

Решите уравнение, пожалуйста!

Answer 1

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

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