If $\alpha,-\frac{\pi}{2}

Question

If $\alpha,-\frac{\pi}{2}<\alpha<\frac{\pi}{2}$ is the solution of $4 \cos \theta+5 \sin \theta=1$, then the value of $\tan \alpha$ is

$\frac{10-\sqrt{10}}{12}$

$\frac{\sqrt{10}-10}{6}$

$\frac{\sqrt{10}-10}{12}$

$\frac{10-\sqrt{10}}{6}$

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