I'm facing the problem of solving $$\sin(x)+x \cdot \cos(x)=0$$ using $$\tan(x)=\sin(x)/\cos(x)$$ I end at $$x+\tan(x)=0$$ on the other hand, I also tried $\cos(x)= \pm \sqrt{1-\sin^2(x)}$ resulting in $x^2-x^2\cdot \sin^2(x)-\sin^2(x)=0$ OR using $\sin(x)= \pm \sqrt{1-\cos^2(x)}$ I get $1-\cos^2(x)-x^2\cdot \cos^2(x)=0$
In all these cases I have no idea on how to get to a solution like $x=...$. As far is I can see, I should try getting $x$ into the trigonometric functions, but I don't see how I could?
tanks for all your help