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If $\sin x = -\frac{3}{5}$,where $\pi < x < \frac{3\pi}{2}$,then $80(\tan^2 x - \cos x)$ is equal to:

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.

If $\cos x = -\frac{3}{5}$ and $x$ lies in the third quadrant,find the values of the other five trigonometric functions.

Prove that $\cos \left(\frac{3 \pi}{2}+x\right) \cos (2 \pi+x)\left[\cot \left(\frac{3 \pi}{2}-x\right)+\cot (2 \pi+x)\right]=1$.

If $\theta = \frac{17 \pi}{3}$,then $(\tan \theta - \cot \theta) = \dots$

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