Suppose there are three vectors $\sin x,\cos x,\tan x$. Now I'm pretty sure that these lie on the same plane. But can I find any constant coefficients that satisfies $c_1\sin x + c_2\cos x + c_3\tan x =0$? I couldn't. Now please rectify me if there is some way to prove that they are linearly dependent. Or please explain if they aren't linearly dependent how they are lying on the same plane ($xy$ plane) .