Question

Solve the following equation:
${\cos }^{2}x+2\sqrt{2}\cos x\sin x+1=0.$

Answer 1

${\cos }^{2}x+2\sqrt{2}\sin x\cos x+{\sin }^{2}x+{\cos }^{2}x=0$

${2\cos }^{2}x+\sqrt{2}\sin x\cos x+\sqrt{2}\sin x\cos x+{\sin }^{2}x=0$

$\sqrt{2}\cos x(\sqrt{2}\cos x+\sin x)+\sin x(\sqrt{2}\cos x+\sin x)=0$

So, ${(\sqrt{2}\cos x+\sin x)}^2=0$
$\tan x=-\sqrt{2},x=n\pi -{\tan }^{-1}\left(\sqrt{2}\right)$