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Which of the following statements is incorrect?

If $\tan \theta = - \frac{1}{\sqrt{10}}$ and $\theta$ lies in the fourth quadrant,then $\cos \theta = $

Suppose $ABC$ is a triangle and $D, E$ are points on the sides $AB$ and $AC$ respectively. If $AD : AB = 3 : 5$ and $AE : AC = 2 : 3$,then the ratio of the areas of the triangles $ABC$ and $ADE$ lies in the interval.

Factorize the expression: $2 \cot^2 \theta - \cot \theta - 3$.

$\frac{1}{\cos 290^{\circ}}+\frac{1}{\sqrt{3} \sin 250^{\circ}} = $

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