ANSWER:
[tex]x=\arctan (a)[/tex]STEP-BY-STEP EXPLANATION:
We have the following equation:
[tex]a\cdot\: \cos \: x-\: \: \sin \: x\: =\: 0[/tex]We solve for x:
[tex]\begin{gathered} a\cdot\: \frac{\cos\: x}{\cos x}-\: \: \frac{\sin\: x}{\cos x}\: =\: \frac{0}{\cos x} \\ a-\tan x=0 \\ \tan x=a \\ x=\arctan (a) \end{gathered}[/tex]