I know that it would be:

$\cos^2\alpha+3\cos^2\alpha=1$ by identities

then it would be:

$4\cos^2\alpha=1$

dividing $4$ to both sides:

$\cos^2\alpha=\frac{1}{4}$

square both sides:

$\cos\alpha=\pm\frac{1}{2}$

After this, what should I do?