$\tan ^{-1} 2+\tan ^{-1} 3=$

If $\tan^{-1}(1) + \tan^{-1}(3) + \tan^{-1}(5) + \tan^{-1}(1/4) = \pi + \tan^{-1}(\alpha/2)$, then the value of $\alpha$ is... (in $/41$)

Let $f(\theta) = \sin ( \tan ^{-1} ( \frac{\sin \theta}{\sqrt{\cos 2 \theta}} ) )$,where $-\frac{\pi}{4} < \theta < \frac{\pi}{4}$,then the value of $\frac{d}{d(\tan \theta)}(f(\theta))$ is

If $\sin ^{-1} \frac{x}{5}+\sin ^{-1} \frac{4}{5}=\frac{\pi}{2}$,then $x=$ . . . . . . .

If $2 \operatorname{Tanh}^{-1} x = \operatorname{Sinh}^{-1}\left(\frac{4}{3}\right)$, then $\operatorname{Cosh}^{-1}\left(\frac{1}{x}\right) = $

If $\tan^{-1} (x+ 2)+ \tan^{- 1}( x -2)= \tan^{-1} (\frac{1}{2}),$ then the sum of the value$(s)$ of $x$ is equal to-