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

$\sin \left( {\frac{\pi }{{10}}} \right)\sin \left( {\frac{{3\pi }}{{10}}} \right) = $

Which of the following is correct

If $x{\sin ^3}\alpha + y{\cos ^3}\alpha = \sin \alpha \cos \alpha $ and $x\sin \alpha - y\cos \alpha = 0,$ then ${x^2} + {y^2} = $

If $x + \frac{1}{x} = 2\cos \alpha $, then ${x^n} + \frac{1}{{{x^n}}} = $

The value of $\cot \frac{\pi}{24}$ is :