In $\triangle ABC$,if $\angle C = 90^{\circ}$,then $\frac{(\sin^2 A + \sin^2 B)}{(\sin^2 A - \sin^2 B)} \sin(A - B) = $

The value of $\cot 70^{\circ} + 4 \cos 70^{\circ}$ is

If $5 \sinh x - \cosh x = 5$,then one of the values of $\tanh x$ is

The number of solutions of the equation $2 \cos(e^x) = 5^x + 5^{-x}$ is:

Let $\tan \alpha, \tan \beta$ and $\tan \gamma$ (where $\alpha, \beta, \gamma \neq \frac{(2n-1)\pi}{2}, n \in N$) be the slopes of three line segments $OA, OB$ and $OC$ respectively,where $O$ is the origin. If the circumcentre of $\Delta ABC$ coincides with the origin and its orthocentre lies on the $y$-axis,then the value of $\left(\frac{\cos 3\alpha + \cos 3\beta + \cos 3\gamma}{\cos \alpha \cos \beta \cos \gamma}\right)^2$ is equal to:

If $\cosh 2x = 199$,then $\coth x$ equals