Giải thích các bước giải:

Ta có:

$\cot\alpha=-a$

$\to\cot^2\alpha=a^2$

$\to\dfrac{\cos^2\alpha}{\sin^2\alpha}=a^2$

$\to \dfrac{\sin^2\alpha}{\cos^2\alpha}=\dfrac1{a^2}$

$\to \dfrac{\sin^2\alpha}{\cos^2\alpha}+1=\dfrac1{a^2}+1$

$\to\dfrac1{\cos^2\alpha}=\dfrac{a^2+1}{a^2}$

$\to \cos^2\alpha=\dfrac{a^2}{a^2+1}$

$\to \cos\alpha=\pm\dfrac{a}{\sqrt{a^2+1}}$