Domain of $\cos ^{-1}\left[\log _5\left(x^2+7 x+15\right)\right]$ is

If $\sum\limits_{n=1}^k \tan ^{-1}\left(\frac{1}{n^2+3 n+3}\right)=\tan ^{-1} \alpha$, then $\alpha=$

The set of values of $x$ such that $\tan ^{-1}\left(\frac{x}{x-2}\right)-\tan ^{-1}\left(\frac{x}{2 x-1}\right)=\tan ^{-1}\left(\frac{2}{3}\right)$ is

If $\sinh \left(2 \tanh ^{-1} x\right)=\frac{11}{60}$, then $x=$