![\bf cos^2(x)+2cos(x)+1=0\implies \stackrel{\textit{let's notice, this is simply }ax^2+bx+c=0}{[cos(x)]^2+2cos(x)+1=0} \\[2em] [cos(x)+1][cos(x)+1]=0 \\\\[-0.35em] ~\dotfill\\\\ cos(x)+1=0\implies cos(x)=-1\implies x=cos^{-1}(-1)\implies \stackrel{\textit{for the range }[0,2\pi ]}{x=\pi } \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{\textit{all solutions}}{x=\pi +2\pi n~~,~~ n \in \mathbb{Z}}~\hfill](/tpl/images/0156/2393/94a86.png)
Find all solutions to the equation.
cos^2x + 2 cos x + 1 = 0...
Answers: 1
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