Question 1095722
<br>Tutor ikleyn's answers are usually reliable; but she missed something here.  Since she didn't show any work in her response to your question, I don't know how she arrived at her incorrect answer.<br>
{{{tanx = -sqrt(2)*sinx}}}
{{{sinx/cosx + sqrt(2)*sinx = 0}}}
{{{sinx(1/cosx+sqrt(2)) = 0}}}
{{{sinx=0}}} or {{{1/cosx=-sqrt(2)}}}<br>
{{{sinx=0}}} gives {{{x=0}}} and {{{x=pi}}}, as shown in ikleyn's response.<br>
{{{1/cosx=-sqrt(2)}}} gives the two additional solutions {{{x = 3pi/4}}} and {{{5pi/4}}}<br>
Graphing the two expressions with a graphing calculator confirms the four solutions.